NEWS RELEASE
FOR IMMEDIATE RELEASE

FOR ADDITIONAL INFORMATION FROM INFINITY, INC., PLEASE CONTACT:
STANTON E. ROSS, PRESIDENT/CEO
(620) 431-6200
JAMES W. DEAN, VICE PRESIDENT, STRATEGIC & CORPORATE DEVELOPMENT
(720) 932-7800
WWW.INFINITY-RES.COM

   INFINITY, INC. REPORTS 2004 THIRD QUARTER AND NINE MONTH FINANCIAL RESULTS

                     Record Quarterly and Nine Month Revenue
            Positive Net Income for the Three and Nine Month Periods
           Quarterly Revenue Increased 26% Over the Prior Year Period

DENVER and CHANUTE, Kan. - (PR Newswire) - November 16, 2004 - Infinity, Inc.
(NASDAQ: IFNY) today announced its financial results for the three months and
nine months ended September 30, 2004. Financial and operational tables follow
this commentary.

THREE MONTH RESULTS

Infinity reported revenue of $6.6 million for the three months ended September
30, 2004, a 26% increase over the $5.2 million reported in the prior year
period.

Oilfield services provided by Consolidated Oil Well Services, Inc.
("Consolidated") generated revenue of $4.8 million during the third quarter of
2004, a 32% increase over the $3.7 million in the prior year period.
Consolidated performed 1,448 cementing, acidizing and fracturing jobs during the
third quarter, a 24% increase over the 1,166 cementing, acidizing and fracturing
jobs in the prior year period. The increase in jobs performed was due to an
additional 318 cement jobs (59% increase), and 113 acidizing jobs (44%
increase), offset by 149 less fracturing jobs (40% decrease). The increase in
revenue was due primarily to the increase in cementing and acidizing jobs, an
increase in revenue per job, and the acquisition of substantially all of the
assets of Blue Star Acid Services, Inc. in late April, partially offset by a
decrease in fracturing jobs.

Exploration and production provided by Infinity Oil & Gas of Wyoming, Inc.
("Infinity-Wyoming") generated revenue of $1.8 million during the third quarter
of 2004, a 13% increase over the $1.6 million in the prior year period.
Infinity-Wyoming produced 317 million cubic feet of gas equivalent ("MMcfe")
during the third quarter of 2004 as compared to 316 MMcfe produced in the second
quarter of 2004 and 340 MMcfe produced in the prior year period. The slightly
higher third quarter production as compared to the second quarter was due to
partial quarter production from new wells brought on line during the third
quarter of 2004, mostly offset by natural production declines in producing
wells.

                                       1


Gross profit for the third quarter of 2004 was $3.5 million, a 28% increase over
the $2.8 million in the prior year period. The increase in gross profit from the
prior year period resulted primarily from the increase in revenue and gross
profit at Consolidated, as well as an increase in revenue and gross profit at
Infinity-Wyoming.

The net income for the third quarter of 2004 was $3.1 million (or $0.29 per
diluted and $0.33 per basic share). For the previous year period, the net loss
was $4.5 million (or $0.55 per basic and diluted share). The $7.6 million
increase in net income over the prior year period was due to: (i) a decrease in
amortization of loan costs of $4.3 million, partially offset by an increase in
depletion of oil and gas assets of $0.3 million; (ii) a gain of $2.8 million in
the third quarter of 2004 primarily due to the previously announced partial sale
of selected assets by Consolidated; (iii) a $0.6 million increase in
Consolidated gross profit and a $0.1 million increase in Infinity-Wyoming gross
profit, partially offset by a $0.1 million increase in operating expenses; and
(iv) a decrease in interest expense of $0.2 million due to less indebtedness and
generally lower interest rates.

Earnings before interest, taxes, depreciation and amortization ("EBITDA") for
the third quarter of 2004 were $2.2 million, a 44% increase over the $1.5
million in the prior year period. A reconciliation of net income to EBITDA, a
non-GAAP figure, is provided in the financial tables following this commentary.

NINE MONTH RESULTS

Infinity reported revenue of $15.2 million for the nine months ended September
30, 2004, a 10% increase over the $13.8 million in the prior year period.

For the first nine months of 2004, Consolidated generated revenue of $10.4
million, a 21% increase over the $8.5 million in the prior year period.
Consolidated performed 3,169 cementing, acidizing and fracturing jobs, a 15%
increase over the 2,745 cementing, acidizing and fracturing jobs in the
prior-year period. The increase in jobs performed was due to an additional 700
cement jobs (57% increase), and 13 acidizing jobs (2% increase), offset by 289
less fracturing jobs (35% decrease). The increase in revenue was due primarily
to the increase in cementing and acidizing jobs, an increase in revenue per job,
and the acquisition of substantially all of the assets of Blue Star Acid
Services, Inc. in late April, partially offset by a decrease in fracturing jobs.


                                       2


Infinity-Wyoming generated revenue of $4.8 million during the first nine months
of 2004, a 9% decrease from the $5.3 million in the prior year period.
Infinity-Wyoming produced 892 MMcfe during the first nine months of 2004 as
compared to 1,167 MMcfe produced in the prior year period. The decrease in first
nine months 2004 revenue versus the 2003 period was due to the 24% decline in
gas equivalent production from the prior year period that resulted primarily
from natural declines in wells producing in 2003 more than offsetting added
production from new wells brought on line in 2004.

Gross profit for the first nine months of 2004 was $7.7 million, an 11% increase
over the $6.9 million in the prior year period. A 19% increase in Consolidated's
gross profit accounted for increase in gross profit, as Infinity-Wyoming's gross
profit was essentially the same as the prior year period.

The net income for the first nine months of 2004 was $0.3 million (or $0.03 per
basic and diluted share). For the previous year period, the net loss was $5.4
million (or $0.67 per basic and diluted share). The $5.6 million increase in net
income over the prior year period was due to: (i) a decrease in amortization of
loan costs of $3.6 million, partially offset by an increase in depreciation,
depletion and amortization expense of $1.6 million due almost entirely to higher
oil and gas depletion; (ii) a gain of $2.7 million in the third quarter of 2004
primarily due to the previously announced partial sale of selected assets by
Consolidated; (iii) a $0.8 million increase in Consolidated gross profit,
partially offset by a $0.1 million increase in operating expenses; and (iv) a
decrease in interest expense of $0.2 million due to less indebtedness and
generally lower interest rates.

EBITDA for the first nine months of 2004 were $3.6 million, a 20% increase over
the $3.0 million in the prior year period, primarily due to an increase in gross
profit from Consolidated offset by a slight increase in operating expense during
the first nine months of 2004 as compared to the prior year period. A
reconciliation of net income to EBITDA, a non-GAAP figure, is provided in the
financial tables following this commentary.

CONFERENCE CALL REMINDER

The Company will host a conference call tomorrow morning, Tuesday, November 16,
2004, at 9:30 a.m. Eastern Standard Time to discuss the reported financial and
operating results in greater detail. The dial-in number for the call is
800-289-0544 (international participants should dial 913-981-5533). Parties
interested in participating in the conference call should dial in approximately
ten minutes prior to the start time. The call will also be broadcast live on the
Internet at http://www.vcall.com/CEPage.asp?ID=89944.


                                       3


A replay of the conference call will be available approximately two hours after
the completion of the call through November 29, 2004, by dialing 888-203-1112
(international callers should dial 719-457-0820) and entering the access code ID
#915000. The call will also be archived for two weeks at
http://www.vcall.com/CEPage.asp?ID=89944.

ABOUT INFINITY, INC.

Infinity, Inc., through its wholly-owned subsidiaries Infinity Oil & Gas of
Wyoming, Inc. and Infinity Oil and Gas of Texas, Inc., is an independent energy
company engaged in the exploration, development and production of natural gas
and oil and the operation and acquisition of natural gas and oil properties. The
Company's current operations are principally focused on the development and
expansion of its producing Wamsutter Arch (Pipeline) project and emerging
Labarge coal bed methane project, both of which are located in the Greater Green
River Basin in southwest Wyoming. Infinity Oil & Gas of Wyoming also holds
exploration and development rights in the Sand Wash and Piceance Basins
principally in northwest Colorado. Infinity Oil and Gas of Texas holds
leaseholds in the Fort Worth Basin of Texas. Infinity, Inc. provides oilfield
services through its wholly-owned subsidiary, Consolidated Oil Well Services,
Inc., with operations principally focused in the Mid-Continent region. The
Company's common stock is listed on the NASDAQ National Market under the symbol
"IFNY."

                                       4





                         INFINITY, INC. AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEETS



                                                                SEPT. 30, 2004 DECEMBER 31, 2003
                                                                 ------------    ------------
                                                                  (unaudited)
                        ASSETS
Current assets

                                                                           
   Cash and cash equivalents                                     $  2,414,788    $    727,134
   Accounts receivable, less allowance for doubtful accounts        3,642,058       1,766,642
   Current portion of note receivable                               1,584,938          16,311
   Inventories                                                        249,335         351,197
   Prepaid expenses and other                                         646,330         206,314
   Derivative asset                                                        --          97,624
                                                                 ------------    ------------
       Total current assets                                         8,537,449       3,165,222

Property and equipment, at cost, less accumulated depreciation      9,289,136      10,169,159
Oil and gas properties, using full cost accounting net of
   accumulated depreciation, depletion, amortization and
   ceiling writedown
     Subject to amortization                                       27,849,851      23,446,343
     Not subject to amortization                                   12,784,201      12,815,834
Intangible assets, at cost, less accumulated amortization           1,978,449       3,952,989
Note receivable, less current portion                                      --       1,580,742
Other assets, net                                                     157,496         135,989
                                                                 ------------    ------------

Total assets                                                     $ 60,596,582    $ 55,266,278
                                                                 ============    ============

            LIABILITIES AND STOCKHOLDERS' EQUITY

Current liabilities

   Notes payable                                                 $    337,288    $         --
   Notes payable - related party                                    1,750,000              --
   Current portion of long-term debt                                1,607,221       1,762,777
   Accounts payable                                                 1,767,807       2,645,277
   Accrued expenses                                                 1,988,817         966,769
                                                                 ------------    ------------
       Total current liabilities                                    7,451,133       5,374,823

Long-term liabilities

   Production taxes payable                                           353,645         229,889
   Asset retirement obligations                                       555,014         520,638
   Long-term debt, less current portion                            10,233,466       9,252,872
   8% subordinated convertible notes payable                        2,643,000       2,793,000
   7% subordinated convertible notes payable                       11,575,000      11,184,000
   Note payable - related party                                            --       3,000,000
                                                                 ------------    ------------
       Total liabilities                                           32,811,258      32,355,222
                                                                 ------------    ------------

Stockholders' equity

   Common stock, par value $.0001, authorized 300,000,000
shares, issued and outstanding 9,422,284 (2004) and
     8,204,032 (2003) shares                                              942             820
   Additional paid-in-capital                                      37,438,334      32,720,904
   Accumulated other comprehensive income                                  --          97,624
   Accumulated deficit                                             (9,653,952)     (9,908,292)
                                                                 ------------    ------------
       Total stockholders' equity                                  27,785,324      22,911,056
                                                                 ------------    ------------

Total liabilities and stockholders' equity                       $ 60,596,582    $ 55,266,278
                                                                 ============    ============



                                       5





                         INFINITY, INC. AND SUBSIDIARIES
                CONSOLIDATED STATEMENTS OF OPERATIONS (UNAUDITED)


                                                  FOR THE THREE MONTHS            FOR THE NINE MONTHS
                                                    ENDED SEPT. 30,                ENDED SEPT. 30,
                                              ----------------------------    ----------------------------
                                                  2004            2003            2004            2003
                                              ------------    ------------    ------------    ------------
Revenue
                                                                                  
   Oil and gas service operations             $  4,842,799    $  3,678,867    $ 10,382,429    $  8,552,827
   Oil and gas sales                             1,762,824       1,562,639       4,835,676       5,296,729
                                              ------------    ------------    ------------    ------------
     Total revenue                               6,605,623       5,241,506      15,218,105      13,849,556
                                              ------------    ------------    ------------    ------------

Cost of revenue

   Oil and gas service operations                2,358,669       1,823,966       5,636,335       4,556,122
   Oil and gas production expenses                 497,844         489,785       1,335,429       1,783,065
   Oil and gas production taxes                    206,980         163,444         558,192         589,793
                                              ------------    ------------    ------------    ------------
     Total cost of revenue                       3,063,493       2,477,195       7,529,956       6,928,980
                                              ------------    ------------    ------------    ------------

Gross profit                                     3,542,130       2,764,311       7,688,149       6,920,576

Operating expenses                               1,352,075       1,259,893       4,178,225       4,028,375
Depreciation, depletion and amortization         1,161,334         848,723       3,523,162       1,928,250
                                              ------------    ------------    ------------    ------------

Operating income (loss)                          1,028,721         655,691         (13,238)        963,851

Other income (expense)

   Interest and other income                        34,300          35,961         111,332         114,737
   Amortization of loan costs                     (400,701)     (4,658,145)     (1,674,798)     (5,302,269)
   Interest expense and finance charges           (327,874)       (538,321)       (917,088)     (1,120,751)
   Gain (loss) on sale of assets                 2,786,786         (23,392)      2,748,132         (27,086)
                                              ------------    ------------    ------------    ------------
     Total other income (expense)                2,092,511      (5,183,897)        267,578      (6,335,369)
                                              ------------    ------------    ------------    ------------

Net income (loss) before income taxes            3,121,232      (4,528,206)        254,340      (5,371,418)

Income tax expense (benefit)                            --              --              --              --
                                              ------------    ------------    ------------    ------------

Net income (loss)                             $  3,121,232    $ (4,528,206)   $    254,340    $ (5,371,418)
                                              ============    ============    ============    ============

Basic net income (loss) per common            $       0.33    $      (0.55)   $       0.03    $      (0.67)
                                              ============    ============    ============    ============

Diluted net income (loss) per common          $       0.29    $      (0.55)   $       0.03    $      (0.67)
                                              ============    ============    ============    ============

Weighted average basic shares outstanding
                                                 9,399,290       8,178,003       9,330,546       7,998,635
                                              ============    ============    ============    ============


Weighted average diluted shares outstanding
                                                11,600,675       8,178,003       9,514,622       7,998,635
                                              ============    ============    ============    ============



                                       6





                         INFINITY, INC. AND SUBSIDIARIES
                 CONSOLIDATED STATEMENT OF CASH FLOW (UNAUDITED)

                                                                    FOR THE NINE MONTHS
                                                                      ENDED SEPT. 30,
                                                               ----------------------------
                                                                   2004            2003
                                                               ------------    ------------

Cash flows from operating activities
                                                                         
   Net income (loss)                                           $    254,340    $ (5,371,418)
                                                               ------------    ------------
   Adjustments to reconcile net income (loss) to net
    cash provided by operating activities
     Depreciation, depletion and amortization                     3,523,162       1,928,250
     Amortization of loan costs included in interest expense      1,674,798       5,302,269
     Gain (loss) on sale of assets                               (2,748,132)         27,086

     Change in assets and liabilities
       (Increase) decrease in accounts receivable                (1,835,416)       (396,666)
       (Increase) decrease in inventories                           101,862         (41,593)
       (Increase) decrease in prepaid expenses                      (81,383)        (29,852)
       Increase (decrease) in accounts payable                     (707,939)     (1,444,817)
       Increase in accrued expenses                               1,429,114         666,788
                                                               ------------    ------------
         Net cash provided by operating activities                1,610,406         640,047
                                                               ------------    ------------

Cash flows from investing activities
   Proceeds from sale of property and equipment                   4,489,550          44,211
   Investment in oil and gas properties                          (6,349,150)     (3,551,079)
   Investment in other assets and intangibles                       (92,885)       (685,545)
   Purchase of property and equipment                            (1,818,699)       (447,746)
   Payments on note receivable                                       12,115          11,218
                                                               ------------    ------------
         Net cash used in investing activities                   (3,759,069)     (4,628,941)
                                                               ------------    ------------

Cash flows from financing activities
   Proceeds from notes payable                                      295,000      11,452,861
   Proceeds from borrowings on long-term debt                     5,844,558              --
   Proceeds from issuance of common stock                         4,095,315         820,482
   Equity issuance costs                                            (30,256)             --
   Repayment of notes payable                                      (485,876)             --
   Repayment of debt                                             (5,882,424)     (7,814,930)
                                                               ------------    ------------
         Net cash provided by financing activities                3,836,317       4,458,413
                                                               ------------    ------------

Net increase in cash and cash equivalents                         1,687,654         469,519

Cash and cash equivalents, beginning of period                      727,134         867,017
                                                               ------------    ------------

Cash and cash equivalents, end of period                       $  2,414,788    $  1,336,536
                                                               ============    ============


                                       7





                         INFINITY, INC. AND SUBSIDIARIES
         SELECTED OPERATING AND FINANCIAL DATA BY SUBSIDIARY (UNAUDITED)

                                                                                              FOR THE NINE MONTHS
                                                       FOR THE THREE MONTHS ENDED                ENDED SEPT. 30,
                                                -----------------------------------------    ----------------------
                                                  SEPT. 30,      JUNE 30,       SEPT. 30,
                                                    2004          2004            2003          2004          2003
Consolidated

(Dollars in millions, before cash discounts)

   Job type:
                                                                                              
     Cementing                                       854           945            536         1,923          1,223
     Acidizing                                       369           267            256           715            702
     Fracturing                                      225           165            374           531            820

   Job revenue:

     Cementing                                      $2.8          $2.1            $1.3         $5.8            $3.1
     Acidizing                                      $0.5          $0.3            $0.4         $1.0            $1.0
     Fracturing                                     $1.8          $1.2            $2.1         $4.1            $4.8
     Discounts and eliminations                    ($0.2)        ($0.3)          ($0.1)       ($0.5)          ($0.3)

Infinity-Wyoming Statistics (1)
(Dollars in thousands)

   Production Volumes:

     Natural gas (MMcf)                              265.5         266.7          254.7         735.4          883.6
     Oil and condensate (MBbls)                        8.5           8.2           14.2          26.1           47.2
     Natural gas equivalents (MMcfe; 6:1)            316.7         315.7          340.0         891.7        1,166.6

   Financial Results:

     Natural gas revenue                        $  1,392.1    $  1,385.8     $  1,140.8    $  3,821.6     $  3,856.6
     Oil and condensate revenue                 $    370.6    $    315.8     $    421.8    $  1,014.0     $  1,440.1
       Total revenue                            $  1,762.8    $  1,701.6     $  1,562.6    $  4,835.7     $  5,296.7
     Production expenses                        $    310.1    $    286.4     $    318.1    $    859.4     $  1,169.6
     Production taxes                           $    207.0    $    195.2     $    163.4    $    558.2     $    589.8
     Transportation expense                     $    187.7    $    188.4     $    163.4    $    476.0     $    612.6

   Financial Results, per Mcfe:

     Natural gas revenue                        $      5.24   $      5.20    $      4.48   $      5.20    $      4.36
     Oil and condensate revenue                 $     43.60   $     38.51    $     29.70   $     38.85    $     30.51
     Natural gas equivalent revenue             $      5.57   $      5.39    $      4.60   $      5.42    $      4.54

     Production expenses                        $      0.98   $      0.91    $      0.94   $      0.96    $      1.00
     Production taxes                           $      0.65   $      0.62    $      0.48   $      0.63    $      0.51
     Transportation expense                     $      0.59   $      0.60    $      0.48   $      0.53    $      0.53



      (1)   Includes revenue, expense and operating data only from the Wamsutter
            Arch Pipeline and Labarge fields.


                                       8






                                          INFINITY, INC. AND SUBSIDIARIES
                      NON-GAAP DISCLOSURES: RECONCILIATION OF NET INCOME (LOSS) TO EBITDA (1)

                                                FOR THE THREE MONTHS                 FOR THE NINE MONTHS
                                                  ENDED SEPT. 30,                       ENDED SEPT. 30,
                                                2004             2003              2004             2003
                                            -------------     ------------     -------------     ------------

                                                                                     
   Net income (loss)                        $  3,121,232      $ (4,528,206)    $    254,340      $ (5,371,418)
   Adjustments:
     Depreciation, depletion, amortization     1,161,334           848,723        3,523,162         1,928,250
     Amortization of loan costs                  400,701         4,658,145        1,674,798         5,302,269
     Interest expense and finance charges        327,874           538,321          917,088         1,120,751
     Gain (loss) on sale of assets            (2,786,786)           23,392       (2,748,132)           27,086
                                            -------------     ------------     -------------     ------------
   EBITDA                                   $  2,224,355      $  1,540,375     $  3,621,256      $  3,006,938
                                            ============      ============     ============      ============


      (1)   In this press release, the term "EBITDA" is used. EBITDA is
            equivalent to earnings before interest, income taxes, depreciation,
            depletion and amortization expenses, and gains and losses on the
            sale of other assets. Infinity's management believes EBITDA is an
            important financial measurement tool that provides information about
            the Company's ability to service or incur indebtedness, and pay for
            its capital expenditures. This information differs from measures of
            performance determined in accordance with generally accepted
            accounting principles (GAAP) and should not be considered in
            isolation or as a substitute for measures of performance prepared in
            accordance with GAAP. This measure is not necessarily indicative of
            operating profit or cash flow from operations as determined under
            GAAP and may not be equivalent to similarly titled measures of other
            companies.

                                      # # #


                                       9