<Page>
EXHIBIT 10.4
November 1, 2002
Wisconsin United for Health Foundation, Inc.
c/o Charles Henderson
Davis & Kuelthau, S.C.
111 East Wisconsin Avenue, Suite 1400
Milwaukee, Wisconsin 53202
Ladies and Gentlemen:
We are writing in connection with the Registration Rights Agreement
dated as of March 23, 2001 (the "Agreement") between ourselves and you
concerning the shares of Cobalt Corporation common stock, no par value (the
"Common Stock") which you acquired on that date. All capitalized terms used
herein and not specifically defined will be deemed to have the meanings assigned
in the Agreement.
Pursuant to the Agreement, the Foundation is requesting registration
of 6.5 million outstanding shares of the Company's Common Stock beneficially
owned by the Foundation (the "Secondary Shares"). You and we have agreed that it
is in our mutual interests to provide for opportunistic sales of Common Stock by
the Foundation by means of a Shelf Registration of certain of the Secondary
Shares. We mutually acknowledge that the Foundation has no authority under the
Agreement to demand a Shelf Registration. The purpose of this letter is to set
forth the terms and conditions on which the Company has agreed to cause a Shelf
Registration of the Secondary Shares, all subject to the terms of the Agreement
except as explicitly set forth herein.
Specifically, you and we have agreed as follows:
1. The Company will promptly, at the Company's expense, file a
Shelf Registration Statement on Form S-3 with respect to 6.5 million shares of
the Foundation's Common Stock. The registration statement may also include
500,000 primary shares to be sold from time to time by the Company as the
Company determines. The filing of the Shelf Registration will not be deemed
pursuant to a "Demand" under the Agreement.
2. The Company will use commercially reasonable efforts to keep
the Shelf Registration effective until all the Foundation's shares registered
thereunder have been sold.
3. The Foundation will give the Company written notice of any
intent to sell registered shares. Such notice shall specify whether the proposed
sale will be an Underwritten Offering, and shall disclose the proposed number of
shares to be sold and such other information
<Page>
Wisconsin United for Health Foundation, Inc.
November 1, 2002
Page 2
as is then available concerning the proposed sale. A sale of registered shares
by the Foundation hereunder is sometimes referred to as a "Takedown," and the
notice of intent under this Section 3 as a "Takedown Notice."
4. Upon receipt of a Takedown Notice, the Company will (subject
to Sections 10 and 13 hereof) use its best efforts promptly to prepare and file
with the SEC such prospectus supplement(s) and/or post-effective amendment(s) to
the Shelf Registration as may be necessary in connection with the Foundation's
proposed sale as described in the Takedown Notice. The obligations of the
parties shall conform to the provisions of Section 8 of the Agreement, except as
otherwise provided in this letter agreement. The Company's obligation to file
amendments and/or supplements with respect to the proposed Takedown shall extend
until the earlier of (x) the 60th day after the filing of the necessary
prospectus supplement or the effective date of the necessary post-effective
amendment, as the case may be, with respect to such Takedown (or, if no
prospectus supplement or post-effective amendment is filed with respect to such
Takedown Notice, then the 60th day after the Company's receipt of such Takedown
Notice), or (y) such time as all Registrable Securities covered by the Takedown
Notice shall have been sold (the earlier of (x) or (y) being sometimes referred
to as the "Takedown Termination Date"). The Foundation shall not sell shares
pursuant to a Takedown Notice following the applicable Takedown Termination
Date. The Foundation may not submit a Takedown Notice until at least 90 days
have elapsed from the last preceding Takedown Termination Date.
5. For all purposes under this letter agreement (a) the filing by
the Company with the SEC of the necessary prospectus supplement(s) or (b) the
declaration of effectiveness of the necessary post-effective amendment(s) to the
Shelf Registration, as the case may be, shall be deemed the effecting of a
registration statement, and the date on which the event described in (a) or (b),
as the case may be, occurs will be deemed the effective date of such
registration statement.
6. If the Takedown is to be an Underwritten Offering, then the
Takedown Notice will be treated as a Demand under the Agreement. Without
limiting the generality of the foregoing, all the limitations on the number,
frequency, timing and availability of Demand Registrations contained in Section
2(d) of the Agreement will apply to Underwritten Offerings from the Shelf
Registration (subject to Sections 2(f) and (g) of the Agreement), provided that
for purposes of Section 2(d)(ii) of the Agreement only, a Demand Registration
shall be deemed to be effected on the date the Takedown Notice is given to the
Company. For purposes of Section 2(g) of the Agreement, the Foundation will be
deemed to have withdrawn its Demand if the Underwritten Offering has not been
closed within sixty (60) days after the filing of the necessary prospectus
supplement or the effective date of the necessary post-effective amendment, as
the case may be, with respect to such Takedown.
7. The Company shall pay all "Registration Expenses" (as defined
in the Agreement) of the initial Shelf Registration contemplated hereby
(including Registration Expenses not incurred at the time of the filing of the
registration statement due to the nature of the Registration Statement as a
Shelf Registration but that are incurred at the time of the first
<Page>
Wisconsin United for Health Foundation, Inc.
November 1, 2002
Page 4
Takedown that is an Underwritten Offering), regardless of when such Registration
Expenses are actually incurred.
8. If the Company intends to issue shares covered by the Shelf
Registration in an Underwritten Offering in the absence of a Takedown Notice,
then it will give notice to the Foundation in the manner provided in Section
3(a) of the Agreement. The Foundation may exercise Piggy-Back Rights in the
manner and subject to the conditions set forth in Section 3 of the Agreement.
9. If a Takedown by the Foundation contemplates a sale other than
an Underwritten Offering, then the Takedown shall be treated for all purposes
under the Agreement as if it were a private placement under Section 11 of the
Agreement. Without limiting the generality of the foregoing, all offering
expenses of a Takedown described in the previous sentence including the expenses
of preparing, printing and filing any necessary prospectus supplement and/or
amendment shall be borne by the Foundation. So long as the contemplated sale
price is no less than seventy-five percent (75%) of the closing price per share
of the Company's Stock on the New York Stock Exchange on the date immediately
prior to the date on which the Foundation agrees in writing to sell such shares,
the Company waives any purchase options it may have with respect to such
Secondary Shares under the Agreement, and also waives the notice specified in
the first sentence of Section 11 of the Agreement.
10. The Foundation acknowledges the Company's obligation to
provide disclosure to the public of all material information, and to maintain
dialogue with analysts and investors. The existence and effectiveness of the
Shelf Registration shall not obligate the Company to tailor or restrict its
public communications in any way, except that during the period beginning on the
receipt of a Takedown Notice treated as a Demand under Section 6 of this letter
agreement, and ending on the Takedown Termination Date, the Company agrees that
it will use its best efforts to avoid public announcements, releases or
presentations which in the judgment of counsel to the Company might constitute
"offers," "illegal prospectuses," "free writing," or other improper activity in
connection with a securities offering. The foregoing, and all the provisions of
this letter agreement, are expressly subject to the provisions of Section 6 of
the Agreement concerning Blackout Periods, which shall apply irrespective of
whether sales by the Foundation are deemed to have been made pursuant to a
Demand; and the Company may delay the filing of a prospectus supplement and/or
amendment for a reasonable period after receiving a Takedown Notice if the
Company's counsel deems such delay necessary or reasonably prudent by reason of
communication occurring before receipt of the Takedown Notice.
11. For as long as the Shelf Registration remains effective, the
Foundation will not make sales of Common Stock other than through a Takedown,
without providing the Company evidence reasonably satisfactory to the Company
that the manner of sale complies with the Securities Act of 1933, as amended.
12. The Foundation agrees to pay the reasonable expenses of
preparing and filing any post-effective amendment to the Shelf Registration
necessitated, in the reasonable
<Page>
Wisconsin United for Health Foundation, Inc.
November 1, 2002
Page 4
judgment of the Company's counsel, by acts of, or changes in material
information about, the Foundation.
13. In all other respects, the terms of the Agreement shall apply
to the registration and sale of shares registered pursuant hereto.
Please confirm by signing below that the foregoing correctly sets
forth the agreement between us.
Very truly yours,
COBALT CORPORATION
By: /s/ Gail L. Hanson
------------------
Confirmed:
WISCONSIN UNITED FOR HEALTH
FOUNDATION, INC.
By: /s/ Ben Brancel
---------------