<PAGE>

                                                                  Exhibit 4.1(b)

                                 FIRST AMENDMENT
                                       TO
                           RECAPITALIZATION AGREEMENT

      This First Amendment to Recapitalization Agreement (the "Amendment") is
made and entered into as of the 6th day of December 1999, by and between Rural
Cellular Corporation, a Minnesota corporation (including its successors, assigns
and affiliates "RCC") and Telephone & Data Systems, Inc., a Delaware
corporation, (including its successors, assigns and affiliates, "TDS").

                                R E C I T A L S:

      A.    RCC and TDS entered into that certain Recapitalization Agreement
            dated the 31st day of October 1999 (the "Agreement"); and

      B.    The Parties desire to amend the Agreement for the purpose of
            amending and restating the terms of the Convertible Preferred Stock
            which would be issued by RCC in the event the FCC Recapitalization
            is consummated.

                                   AGREEMENT:

      NOW, THEREFORE, in consideration of the foregoing premises, the mutual
covenants contained herein and for other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties do hereby
agree as follows:

      1. Defined Terms. Capitalized terms used, but not defined herein, shall
have the meaning ascribed thereto in the Agreement.

      2. Amendment and Restatement of Terms of Convertible Preferred Stock.
Exhibit A entitled "Term Sheet for Convertible Preferred Stock" attached to the
Agreement, is hereby amended and restated in its entirety as set forth in the
Amended Exhibit A attached hereto.

      3. Tax Position. TDS acknowledges that RCC's tax advisors have recommended
to RCC that, under the Code, the dividends due at the end of the term of the
Convertible Preferred Stock should not be deemed taxable income to TDS until and
unless the dividends are actually declared at the end of the term. TDS and RCC
agree that the position recommended is justified and agree to file their federal
and other applicable income tax returns in a manner consistent with that
position. If, as a result of an audit or examination of TDS or any of its
subsidiaries, a taxing authority asserts that the dividends payable at the end
of the term of the Convertible Preferred Stock must be accrued and taxed
currently (a "Deemed Dividend " ), then RCC shall pay to TDS a Tax Indemnity
Payment, defined and computed as set forth below, together with any interest and
penalties resulting from such assertion and contest expenses relating thereto.
RCC shall be given prompt notice of any such audit or examination and an
opportunity to participate (at its own expense) in the resolution of any issues
that would affect it, but only to the extent such issue can be separated on
audit from any other tax issues of TDS, and shall reimburse TDS

<PAGE>

for TDS's expenses relating thereto. In the event that TDS chooses not to
challenge the position of the taxing authority, RCC, at its own expense, may
elect to challenge, on behalf of TDS and itself, any adverse position taken by
an applicable taxing authority and for appealing any adverse decisions, but only
to the extent such issue can be separated on audit from any other tax issues of
TDS ; TDS shall cooperate with any such challenge by RCC, at RCC's expense.
Payment of the Tax Indemnity Payment shall be due from RCC only after a final
non-appealable determination with respect thereto or if a further contest
becomes commercially unreasonable. Following such an event (an "Adverse Tax
Determination"), TDS shall no longer be bound by the second sentence of this
section 3.

      4. Tax Indemnity Payments. Following an Adverse Tax Determination , RCC
shall pay to TDS an annual Tax Indemnity Payment equal to 0.24% of the face
amount of the outstanding Convertible Preferred Stock owned by TDS for each year
covered by the Adverse Tax Determination and all future periods during which the
Convertible Preferred Stock is outstanding. The Tax Indemnity Payment shall be
paid by RCC immediately following the Adverse Tax Determination in the case of
prior periods and, in the case of future periods , on or before January 15 of
the year following the year for which each Deemed Dividend is deemed to have
accrued.

      5. Confirmation of Agreement. Except as set forth in this Amendment, the
provisions of the Agreement are hereby ratified, confirmed and approved in all
respects as if fully set forth herein.

      IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
executed by duly authorized representatives as of the day, month and year first
above written.

                                       RURAL CELLULAR CORPORATION


                                       By   /s/ Richard P. Ekstrand
                                       Its   President


                                       TELEPHONE & DATA SYSTEMS, INC.


                                       By   /s/ LeRoy T. Carlson
                                       Its   Chairman



    Signature page to First Amendment to Recapitalization Agreement relating
         to Telephone & Data Systems, Inc.'s ownership interest in Rural
                              Cellular Corporation
                             dated December 6, 1999.


                                       2
<PAGE>

                                AMENDED EXHIBIT A

                   TERM SHEET FOR CONVERTIBLE PREFERRED STOCK

o     Class: The convertible preferred stock shall be a separate class of
      preferred stock. Only TDS, affiliates of TDS or TDS Owned Entities or
      their respective successors and assigns shall hold such separate class of
      preferred stock.

o     Date of Issuance: Issuance of the convertible preferred stock shall be
      conditioned upon the FCC's acceptance of the issuance of such convertible
      preferred stock as a remedy for the Cross-Ownership Issues (the "FCC
      Closing Date").

o     Liquidation Preference: The convertible preferred stock shall have a
      liquidation preference of $1,000.00 per share.

o     Amount: The Excess Shares shall be exchangeable for that number of shares
      of convertible preferred stock determined by dividing the product of $50
      5/8 (the RCC common stock price as of October 22, 1999) times the number
      of Excess Shares by $1,000.00.

o     Term: The preferred stock is mandatorily redeemable by the Company for
      cash on the first day following the twentieth (20th) anniversary of the
      date of issuance.

o     Payment of Dividends: Dividends on the convertible preferred stock shall
      be cumulative, with a fixed coupon rate of four percent (4%) per annum.
      Dividends would be payable at the end of the term , at which point they
      would be declared and paid unless prohibited by law. In the event of
      conversion prior to the end of the term , dividends would not be declared.
      The convertible preferred stock will also participate on a current basis
      in dividends, if any, declared with respect to the Company's Class A
      Common Stock or Class B Common Stock.

o     Conversion: The convertible preferred stock shall convert in the aggregate
      into the same number of shares of Class A and Class B Common Stock as the
      number of Excess Shares originally exchanged. Partial conversions shall be
      effected on a proportionate basis. The Non-Dilution Provision shall apply.
      The convertible preferred stock shall be convertible at any time prior to
      the twentieth (20th) anniversary at the option of either TDS or the
      Company, in whole or in part, so long as the issuance of shares of the
      Company's Class A Common Stock and/or Class B Common Stock shall not
      violate the then applicable FCC rules on cross-ownership.

o     Subordination: The convertible preferred stock shall be subordinate, at
      the option of the Company as exercised from time to time, to any or all
      classes of preferred stock and debt, whether now outstanding or hereafter
      issued, with respect to the liquidation preference and the payment of
      dividends.

<PAGE>

o     Transferability: The convertible preferred stock shall be transferable by
      TDS to the extent permitted under applicable securities laws, provided
      that notice of any proposed transfer must be provided to the Company at
      least 30 days in advance and, if the Company so requires, an opinion of
      counsel satisfactory to the Company that such transfer does not violate
      the registration requirements of federal or state securities laws, and,
      further provided, that such transfer shall not be in violation of any FCC
      rule nor result in a Cross Ownership Issue between RCC and the transferee.
      To the extent that any shares of convertible preferred stock which are
      convertible into Class B Common Stock are transferred to a person that is
      not an affiliate of TDS (as the term "affiliate" is defined in RCC's
      Articles of Incorporation,) such share(s) of convertible preferred stock
      transferred shall thereafter be convertible only into Class A Common
      Stock. The conversion rights will not be transferable separate from the
      convertible preferred stock.

o     Registration Rights: The convertible preferred stock shall not be
      registered under federal or state securities laws.


                                       2