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                                                                   Exhibit 10.34

                              REDEMPTION AGREEMENT

        THIS REDEMPTION AGREEMENT (this "Agreement") is made as of December 11,
2000, among N2H2, INC., a Washington corporation (the "Company"), and the
marital community of KEVIN Fink and JESSICA LYMAN, residing at 103 NW 49th
Street, Seattle, Washington 98107 (collectively, the "Shareholder").

                                    RECITALS

        WHEREAS, the Shareholder owns seven hundred thirty-five thousand
(735,000) shares of the Company's common stock, no par value (the "Shares"), all
or a portion of which the Shareholder wishes to have the Company redeem, and the
Company is willing to redeem those Shares, on the terms and conditions set forth
in this Agreement; and

        WHEREAS, the Company has advanced for the benefit of the Shareholder the
sum of $443,390.14, and the Shareholder's obligation to repay the Advance is
evidenced by a certain Promissory Note dated November 1, 2000 (the "Note"); and

        WHEREAS, the parties wish to provide in all events for repayment of the
principal balance of the Note and all accrued interest thereon (such amounts as
of any particular date will be referred to as the "Note Balance") by a
redemption of a portion of the Shares according to terms and conditions of this
Agreement.

        NOW, THEREFORE, it is agreed as follows:

        1. REDEMPTION FOR PAYMENT OF NOTE BALANCE.

               1.1 TENDER OF SHARES. On any date or dates prior to December 31,
2000, the Shareholder may elect to tender Shares to the Company for redemption
hereunder and application of the redemption proceeds to payment of the Note
Balance by hand-delivering to the Company at 900 Fourth Avenue, Suite 3400,
Seattle, Washington 98164, or such other address as the Company may hereafter
designate from time to time by written notice to the Shareholder (a) a written
notice (the "Notice") specifying the number of Shares to be redeemed (the
"Tendered Shares") and the date upon which such redemption shall be effective
(the "Redemption Date"), which shall be a day that the securities markets are
open and that is on or after the date the Notice is delivered, and (b) a duly
completed and executed assignment separate from certificate assigning the
Tendered Shares to the Company.

               1.2 REDEMPTION PRICE. As full consideration for redemption of
Tendered Shares on a Redemption Date, the Company shall apply to the Note
Balance, effective as of the Redemption Date, for each of the Tendered Shares
redeemed an amount (the "Redemption Price") equal to the greater of (a) one
dollar ($1.00) or (b) the closing sales price for the Company's common stock on
the Redemption Date, as reported by the Nasdaq Stock Market; PROVIDED, HOWEVER,
if the aggregate Redemption Price for the Tendered Shares on a Redemption Date
exceeds the Note Balance, then the number of Tendered Shares shall be reduced to
the smallest whole number of shares the redemption of which at the Redemption
Price will result in full payment of the Note Balance, and the additional Shares
specified in the Notice but not

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redeemed shall be treated as "Additional Shares" and shall be deemed to have
been tendered as for purposes of Section 2.1.

               1.3 AUTOMATIC REDEMPTION TENDER. If the Note Balance has not been
paid in full prior to December 31, 2000, by means of the redemption of Tendered
Shares in accordance with the preceding provisions of this Section 1 or
otherwise, then there are hereby tendered to the Company by the Shareholder for
redemption on December 31, 2000, at the Redemption Price for that date, the
smallest whole number of Shares the redemption of which at such Redemption Price
will result in full payment of the Note Balance. The Shareholder is delivering
to the Company upon execution of this Agreement an assignment separate from
certificate substantially in the form attached as Exhibit A duly executed by the
Shareholder (the "Assignment"). The Shareholder hereby authorizes the Company to
complete the Assignment as necessary to transfer Shares to facilitate the
redemption under this Section 1.3.

        2. REDEMPTION OF ADDITIONAL SHARES.

               2.1 REMAINING SHARES. At any time or times following full payment
of the Note Balance and prior to November 22, 2001 (or if earlier, the return to
the Shareholder pursuant to Section 3 of the certificate(s) for the Shares not
redeemed hereunder), the Shareholder may elect to tender to the Company for
redemption hereunder (an "Additional Tender") any of the Shares not redeemed
pursuant to Section 1 ("Additional Shares") by hand-delivering to the Company at
the address specified or designated as provided in Section 1.1 (a) a written
notice (the "Additional Notice") specifying the number of Additional Shares to
be redeemed (the "Tendered Additional Shares") and the date upon which such
redemption shall be effective (the "Additional Redemption Date"), which shall be
a day that the securities markets are open and that is on or after the date the
Additional Notice is delivered, and (b) a duly completed and executed assignment
separate from certificate assigning the Tendered Additional Shares to the
Company.

               2.2 CONSIDERATION. As full consideration for redemption of
Additional Shares on an Additional Redemption Date, the Company shall pay to the
Shareholder, within three (3) business days after the Additional Redemption
Date, for each of the Tendered Additional Shares redeemed, an amount equal to
ninety percent (90%) of the closing sales price for the Company's common stock
on the Additional Redemption Date, as reported by the Nasdaq Stock Market.

        3. DELIVERY OF CERTIFICATE FOR SHARES. The Shareholder is delivering to
the Company upon execution of this Agreement the certificate(s) for the Shares.
The Company is authorized to deliver such certificate(s), and any additional
certificate(s) issued by the Company's transfer agent following any redemption
hereunder, to the Company's transfer agent, together with appropriate
assignments separate from certificate, in order to facilitate redemption of
Shares pursuant to this Agreement. At any time following December 31, 2000, the
Company will, upon receipt of a written request from the Shareholder, return to
the Shareholder the certificate(s) representing any Additional Shares not
redeemed pursuant hereto.

        4. REPRESENTATIONS AND WARRANTIES OF THE COMPANY. The Company represents
and warrants that (a) all corporate action on the part of the Company necessary
for the authorization, execution, delivery and performance of this Agreement and
the transactions


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contemplated hereby has been taken, (b) no broker, finder or intermediary has
been employed by the Company in connection with this Agreement, and (c) this
Agreement constitutes a valid and legally binding obligation of the Company.

        5. REPRESENTATIONS AND WARRANTIES OF SHAREHOLDER. The Shareholder
represents and warrants as follows:

               5.1 No broker, finder or intermediary has been employed by the
Shareholder in connection with this Agreement; and this Agreement constitutes a
valid and legally binding obligation of the Shareholder.

               5.2 The Shareholder owns the Shares being sold by it hereunder,
has not transferred or attempted to transfer any interest in such Shares to any
person or entity, and has full power and authority to transfer and deliver such
Shares, and such Shares are free and clear of any and all liens, encumbrances,
charges, duties and assessments whatsoever.

        6. MISCELLANEOUS.

               6.1 This Agreement may be amended only by an instrument in
writing signed by the party against whom enforcement of any such amendment is
sought.

               6.2 This Agreement contains the entire agreement and
understanding of the parties with respect to the entire subject matter hereof,
and there are no representations, inducements, promises or agreements, oral or
otherwise, not embodied herein.

               6.3 Each party to this Agreement shall perform any and all acts
and execute and deliver any and all documents as may be necessary and proper
under the circumstances in order to accomplish the intents and purposes of this
Agreement and to carry out its provisions.

               6.4 If any party engages an attorney to enforce the terms of this
Agreement, regardless of whether a lawsuit is commenced, the prevailing party
shall, in addition to any other relief, be entitled to recover all costs and
expenses, including but not limited to attorneys' fees, incurred in connection
therewith, including any such costs and expenses incurred on appeal.

               6.5 This Agreement may be executed in two or more counterparts,
each of which shall be deemed an original, but all of which shall constitute one
and the same instrument. This Agreement shall be effective upon delivery of an
executed counterpart via facsimile transmission by the Company to the
Shareholder and by the Shareholder to the Company.

                            [SIGNATURE PAGE FOLLOWS]

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        I WITNESS WHEREOF, the parties have executed this Agreement effective as
of the date first written above.

"Company"                          N2H2, INC.



                                   By: /s/ PETER H. NICKERSON
                                      ------------------------------------------
                                         Peter H. Nickerson,
                                         President and Chief Executive Officer
"Shareholder"

                                    /s/ KEVIN FINK
                                   ---------------------------------------------
                                   KEVIN FINK

                                    /s/ JESSICA LYMAN
                                   ---------------------------------------------
                                   JESSICA LYMAN



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