EXHIBIT (a)(1)


May 5, 1999

Dear Limited Partner:

       Enstar Income Program 1984-1, L.P. (the "Partnership") and its corporate
general partner, Enstar Communications Corporation (the "General Partner"), have
become aware that an unsolicited offer (the "Offer") to purchase outstanding
units in the Partnership, at a price of $210 per unit, was commenced by Madison
Liquidity Investors 104, LLC ("Madison") pursuant to an offer to purchase dated
April 21, 1999.  THIS OFFER WAS MADE WITHOUT THE CONSENT OR THE INVOLVEMENT OF
THE PARTNERSHIP OR THE GENERAL PARTNER.  The Partnership and the General Partner
have filed with the Securities and Exchange Commission a Recommendation
Statement on Schedule 14D-9, relating to the Offer.  A copy of that
Recommendation Statement on Schedule 14D-9 is enclosed with this letter and we
urge you to review it carefully.

       As more fully described in the Recommendation Statement on Schedule
14D-9, we recommend that you reject Madison's Offer.  We note, however, that
some unitholders may view the Offer as attractive, even if at a low value,
because it offers the prospect of liquidity.  We also note that there can be no
assurance as to when unitholders will be presented with another opportunity to
liquidate their investment in the units. In evaluating the Offer, the
Partnership and the General Partner believe that its limited partners should
also consider the following information:

- -      The Partnership's cash flow (operating income before depreciation and
       amortization) for the twelve months ended December 31, 1998 was
       approximately $79.14 per unit.  The price offered by Madison represents
       a valuation of approximately 2.6 times cash flow (after adjustment for
       the excess of current assets over total liabilities as of December 31,
       1998).  The Partnership and the General Partner believe that a valuation
       of 2.6 times cash flow is considerably lower than the inherent value of
       the Partnership's assets based on cash flow multiples paid for similar
       assets.

- -      As of the date of this letter, the General Partner believes that a
       reasonable range of valuation per limited partnership unit is between
       $380 and $460 based on the factors noted below.  The General Partner
       believes that the Madison Offer is inadequate because it is
       significantly less than the $380 low end of the range provided.  The
       General Partner did not retain a third party to conduct an evaluation of
       the Partnership's assets or otherwise obtain any appraisals.  Rather,
       the per unit valuations provided were derived by attributing a range of
       multiples to the Partnership's cash flow (operating income before
       depreciation and amortization) for the twelve months ended December 31,
       1998, adjusted for the excess of current assets over total liabilities.
       The General Partner has selected market multiples based on, among other
       things, its understanding of the multiples placed on other transactions
       involving comparable cable television properties and the securities of
       companies in that industry.  The General Partner's belief as to the
       valuation range provided is necessarily based on economic, industry and
       financial market conditions as they exist as of the date of this letter,
       all of which are subject to change, and there can be no assurance that
       the Partnership's cable properties could actually be sold at a price
       within this range.  Additionally, the valuations provided do not give
       effect to any

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       brokerage or other transaction fees that might be incurred by the 
       Partnership in any actual sale of the Partnership's systems.

- -      The Partnership and the General Partner believe that secondary market
       prices generally do not reflect the current market value of the
       Partnership's assets, nor are they indicative of total return, since
       prior cash distributions and tax benefits received by the original
       investor are not reflected in the prices.  Nevertheless, the secondary
       market prices, to the extent that the reported data are reliable, are
       indicative of the prices at which the Partnership's units trade in the
       illiquid secondary market.  As reported in THE PARTNERSHIP SPECTRUM, the
       weighted average price was $333.58 per unit for the months of January
       and February 1999 (based on five trades involving an aggregate of 120
       units).  There can be no assurance regarding future secondary market
       prices.

       Furthermore, one of the obligations of the Corporate General Partner is
to endeavor to preserve the status of the Partnership as a partnership under
Federal income tax laws.  Failure to maintain this status could have a material
adverse effect on the Partnership and its partners.  Among the related legal
requirements imposed upon the Partnership is that its partnership interests not
be traded on an established securities market, a secondary market or the
substantial equivalent of a secondary market.  As it believes is customary, the
Partnership complies with this requirement by adhering to an Internal Revenue
Service safe harbor which limits most sales of limited partnership interests to
five percent of the outstanding units in any given year.  AFTER FIVE PERCENT OF
THE OUTSTANDING UNITS HAVE BEEN TRANSFERRED IN 1999, NO FURTHER SALES OF UNITS,
INCLUDING ANY ATTEMPTED SALES RELATED TO THE MADISON OFFER, WILL BE RECOGNIZED
BY THE PARTNERSHIP FOR THE BALANCE OF 1999.

       For the reasons discussed above and more fully described in the
Recommendation Statement on Schedule 14D-9, the Partnership and the General
Partner recommend that you NOT transfer, agree to transfer, or tender any units
in response to the Madison Offer.  To the extent that you have previously
tendered units pursuant to Madison's Offer, we note that you have a right to
withdraw your tender by following the procedures set forth under "Section 5. 
Withdrawal Rights" in Madison's offer to purchase document.

       If you have any questions regarding these matters or your investment,
please call our Investor Services Department at (800) 433-4287.

Sincerely,

Enstar Income Program 1984-1, L.P.
Enstar Communications Corporation

cc:    Account Representative

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