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                                                                     EXHIBIT 4.1

                     ZIX CORPORATION 2001 STOCK OPTION PLAN
                    (AMENDED AND RESTATED AS OF MAY 6, 2003)

    SECTION 1. Purpose. The purpose of the Zix Corporation 2001 Stock Option
Plan (hereinafter called the "2001 Plan") is to advance the interests of Zix
Corporation (hereinafter called the "Company") by strengthening the ability of
the Company to attract, on its behalf and on behalf of its Subsidiaries (as
hereinafter defined), and retain personnel of high caliber through encouraging a
sense of proprietorship by means of stock ownership.

    SECTION 2. Definitions.

    "Board of Directors" shall mean the Board of Directors of the Company.

    "Code" shall mean the Internal Revenue Code of 1986, as amended from
time-to-time.

    "Committee" shall mean a committee of the Board of Directors comprised of at
least two directors or the entire Board of Directors, as the case may be.
Members of the Committee shall be selected by the Board of Directors. To the
extent necessary to comply with the requirements of Rule 16b-3, the Committee
shall consist of two or more Non-employee Directors. Also, if the requirements
of Section 162(m) of the Code are intended to be met, the Committee shall
consist of two or more "outside directors" within the meaning of Section 162(m)
of the Code.

    "Common Stock" shall mean the Common Stock of the Company, par value $.01
per share.

    "Date of Grant" shall mean the date on which an Option is granted pursuant
to this 2001 Plan.

    "Designated Beneficiary" shall mean the beneficiary designated by the
Optionee, in a manner determined by the Committee, to receive amounts due the
Optionee in the event of the Optionee's death. In the absence of an effective
designation by the Optionee, Designated Beneficiary shall mean the Optionee's
estate.

    "Exchange Act" shall mean the Securities Exchange Act of 1934, as amended.

    "Fair Market Value" shall mean the closing sale price (or average of the
quoted closing bid and asked prices if there is no closing sale price reported)
of the Common Stock on the date specified as reported by The Nasdaq Stock
Market, or by the principal national stock exchange on which the Common Stock is
then listed. If there is no reported price information for such date, the Fair
Market Value will be determined by the reported price information for Common
Stock on the day nearest preceding such date.

    "Incentive Stock Option" shall mean a stock option granted under Section 6
that is intended to meet the requirements of Section 422 of the Code (or any
successor provision).

    "Non-employee Director" shall have the meaning given such term in Rule
16b-3.

    "Nonqualified Stock Option" shall mean a stock option granted under Section
6 that is not intended to be an Incentive Stock Option.

    "Option" shall mean an Incentive Stock Option or a Nonqualified Stock
Option.


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    "Optionee" shall mean the person to whom an option is granted under the 2001
Plan or who has obtained the right to exercise an option in accordance with the
provisions of the 2001 Plan.

    "Rule 16b-3" shall mean Rule 16b-3 of the rules and regulations under the
Exchange Act as it may be amended from time-to-time and any successor provision
to Rule 16b-3 under the Exchange Act.

    "Subsidiary" shall mean any now existing or hereafter organized or acquired
corporation or other entity of which fifty percent (50%) or more of the issued
and outstanding voting stock or other economic interest is owned or controlled
directly or indirectly by the Company or through one or more Subsidiaries of the
Company.

    SECTION 3. Administration. The 2001 Plan shall be administered by the
Committee. The Committee shall have sole and complete authority to adopt, alter
and repeal such administrative rules, guidelines and practices governing the
operation of the 2001 Plan as it shall from time-to-time deem advisable, and to
construe, interpret and administer the terms and provisions of the 2001 Plan and
the agreements thereunder. The determinations and interpretations made by the
Committee are final and conclusive.

    SECTION 4. Eligibility. All employees and non-employee consultants and
advisors (other than Non-employee Directors) who, in the opinion of the
Committee, have the capacity for contributing in a substantial measure to the
successful performance of the Company are eligible to receive Options under the
2001 Plan.

    SECTION 5. Maximum Amount Available for Options.

    (a) The maximum number of shares of Common Stock in respect of which Options
may be made under the 2001 Plan shall be a total of 2,525,000 shares of Common
Stock. Of that amount, no participant may be granted Options for more than
1,000,000 shares of Common Stock in the aggregate during the term of the 2001
Plan. Options that expire, lapse or are cancelled or forfeited do not count
against theses share limits. Shares of Common Stock may be made available from
the authorized but unissued shares of the Company or from shares reacquired by
the Company, including shares purchased in the open market. In the event that an
Option is terminated unexercised as to any shares of Common Stock covered
thereby, such shares shall thereafter be again available for award pursuant to
the 2001 Plan.

    (b) In the event that the Committee shall determine that any stock dividend,
recapitalization, reorganization, merger, consolidation, split-up, spin-off,
combination, exchange of shares, warrants or rights offering to purchase Common
Stock at a price substantially below fair market value, or other similar
corporate event affects the Common Stock such that an adjustment is required in
order to preserve the benefits or potential benefits intended to be made
available under the 2001 Plan, then the Committee shall adjust appropriately any
or all of (1) the number and kind of shares which thereafter may be optioned
under the 2001 Plan and (2) the grant, exercise or conversion price and/or
number of shares with respect to the Options and/or, if deemed appropriate, make
provision for cash payment to an Optionee; provided, however, that the number of
shares subject to any Option shall always be a whole number.

    SECTION 6. Stock Options.

    (a) Subject to the provisions of the 2001 Plan, the Committee shall have
sole and complete authority to determine the persons to whom Options shall be
granted, the number of shares to be covered by each Option, the option price
therefor and the conditions and limitations applicable to the exercise of the
Option.


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    (b) The Committee shall have the authority to grant Incentive Stock Options,
or to grant Nonqualified Stock Options, or to grant both types of options. In
the case of Incentive Stock Options, the terms and conditions of such grants
shall be subject to and comply with the Code and relevant regulations. Incentive
Stock Options to purchase Common Stock may be granted to such employees of the
Company or its Subsidiaries (including any director who is also an employee of
the Company or one of its Subsidiaries) as shall be determined by the Committee.
Nonqualified Stock Options to purchase Common Stock may be granted to such
eligible participants as shall be determined by the Committee. Neither the
Company nor any of its Subsidiaries or any of their respective directors,
officers or employees, shall be liable to any Optionee or other person if it is
determined for any reason by the Internal Revenue Service or any court having
jurisdiction that any Incentive Stock Option granted hereunder does not qualify
for tax treatment as an Incentive Stock Option under the then-applicable
provisions of the Code.

    (c) The Committee shall, in its discretion, establish the exercise price at
the time each Option is granted, which in the case of Nonqualified Stock
Options, shall not be less than 100% of the Fair Market Value of the Common
Stock on the Date of Grant, or in the case of grants of Incentive Stock Options,
shall not be less than 100% of the Fair Market Value of the Common Stock on the
Date of Grant or such greater amount as may be prescribed by the Code.

    (d) Exercise

        (1) Each Option shall be exercisable at such times and subject to such
    terms and conditions as the Committee may, in its sole discretion, specify
    in the applicable grant or thereafter; provided, however, that in no event
    may any Option granted hereunder be exercisable after the expiration of ten
    years from the Date of Grant. The Committee may impose such conditions with
    respect to the exercise of Options, including without limitation, any
    relating to the application of federal or state securities laws, as it may
    deem necessary or advisable.

        (2) No shares shall be delivered pursuant to any exercise of an Option
    until payment in full of the option price therefore is received by the
    Company. Such payment may be made in cash, or its equivalent, or, if and to
    the extent permitted by the Committee or under the terms of the applicable
    agreement, by exchanging shares of Common Stock owned by the Optionee (which
    are not the subject of any pledge or other security interest), or by a
    combination of the foregoing, provided that the combined value of all cash
    and cash equivalents and the Fair Market Value of any such Common Stock so
    tendered to the Company, valued as of the date of such tender, is at least
    equal to such option price.

        If the shares to be purchased are covered by an effective registration
        statement under the Securities Act of 1933, as amended, any Option may
        be exercised by a broker-dealer acting on behalf of an Optionee if (a)
        the broker-dealer has received from the Optionee instructions signed by
        the Optionee requesting the Company to deliver the shares of Common
        Stock subject to such Option to the broker-dealer on behalf of the
        Optionee and specifying the account into which such shares should be
        deposited, (b) adequate provision has been made with respect to the
        payment of any withholding taxes due upon such exercise, and (c) the
        broker-dealer and the Optionee have otherwise complied with Section
        220.3(e)(4) of Regulation T, 12 CFR Part 220, or any successor
        provision.

        (3) The Company, in its sole discretion, may lend money to an Optionee,
    guarantee a loan to an Optionee or otherwise assist an Optionee to obtain
    the cash necessary to exercise all or any portion of an Option granted under
    the 2001 Plan.


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        (4) The Company shall not be required to issue any fractional shares
    upon the exercise of any Options granted under this 2001 Plan. No Optionee
    nor an Optionee's legal representatives, legatees or distributees, as the
    case may be, will be, or will be deemed to be, a holder of any shares
    subject to an Option unless and until said Option has been exercised and the
    purchase price of the shares in respect of which the Option has been
    exercised has been paid. Unless otherwise provided in the agreement
    applicable thereto, an Option shall not be exercisable except by the
    Optionee or by a person who has obtained the Optionee's rights under the
    Option by will or under the laws of descent and distribution or pursuant to
    a "qualified domestic relations order" as defined in the Code.

    (e) No Incentive Stock Options shall be exercisable (a) more than five years
(or such other period of time as from time-to-time provided in the
then-applicable provisions of the Code governing Incentive Stock Options) after
the Date of Grant with respect to an Optionee who owns ten percent or more of
the outstanding Common Stock (within the meaning of the Code), and (b) more than
ten years after the Date of Grant with respect to all other Optionees. No
Nonqualified Stock Options shall be exercisable more than ten years after the
Date of Grant.

    (f) In no event shall any Option granted to any employee who is classified
as "non-exempt" under the Fair Labor Standards Act of 1938 be exercisable less
than six months after the Date of Grant, except in the case of death,
disability, retirement, a change in control or other circumstances permitted by
regulations under the Worker Economic Opportunity Act ("WEOA"). Grants to such
non-exempt employees shall not be based on pre-established performance criteria,
except as specifically permitted under the WEOA. Non-exempt employees shall be
notified of the terms of their Options in accordance with the WEOA, and exercise
of such Options must be voluntary.

    SECTION 7. General Provisions.

    (a) The Company and its Subsidiaries shall have the right to deduct from all
amounts paid to an Optionee in cash (whether under the 2001 Plan or otherwise)
any taxes required by law to be withheld in respect of Option exercises under
the 2001 Plan. However, if permitted by the Committee or under the terms of the
applicable agreement, the Optionee may pay all or any portion of the taxes
required to be withheld by the Company or its Subsidiaries or paid by the
Optionee with respect to such Common Stock by electing to have the Company or
its Subsidiaries withhold shares of Common Stock, or by delivering previously
owned shares of Common Stock, having a Fair Market Value equal to the amount
required to be withheld or paid. The Optionee must make the foregoing election
on or before the date that the amount of tax to be withheld is determined. Any
such election is irrevocable and subject to disapproval by the Committee. If the
Optionee is subject to the provisions of Section 16(b) of the Exchange Act, then
any such election shall be subject to the restrictions imposed by Rule 16b-3.

    (b) Each Option hereunder shall be evidenced in writing, delivered to the
Optionee, and shall specify the terms and conditions thereof and any rules
applicable thereto, including, but not limited to, the effect on such Option of
the death, retirement, disability or other termination of employment of the
Optionee and the effect thereon, if any, of a change in control of the Company.

    (c) Unless otherwise provided in the agreement applicable thereto, no Option
shall be assignable or transferable except by will or under the laws of descent
and distribution or pursuant to a "qualified domestic relations order" as
defined in the Code, and no right or interest of any Optionee shall be subject
to any lien, obligation or liability of the Optionee.

    (d) No person shall have any claim or right to be granted an Option.
Further, the Company and its Subsidiaries expressly reserve the right at any
time to terminate the employment of an Optionee free from any liability, or any
claim under the 2001 Plan, except as provided in any agreement entered into with


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respect to an Option. Neither the 2001 Plan nor any Option granted hereunder is
intended to confer upon any Optionee any rights with respect to continuance of
employment or other utilization of his or her services by the Company or by a
Subsidiary, nor to interfere in any way with his or her right or that of his or
her employer to terminate his or her employment or other services at any time
(subject to the terms of any applicable contract). The conditions to apply to
the exercise of an Option in the event an Optionee ceases to be employed by the
Company or a Subsidiary for any reason shall be determined by the Committee or
specified in the written agreement evidencing the Option.

    (e) Subject to the provisions of the applicable Option, no Optionee or
Designated Beneficiary shall have any rights as a stockholder with respect to
any shares of Common Stock to be distributed under the 2001 Plan until he or she
has become the holder thereof.

    (f) The validity, construction, interpretation, administration and effect of
the 2001 Plan and of its rules and regulations, and rights relating to the 2001
Plan, shall be determined solely in accordance with the laws of the State of
Texas (without giving effect to its conflicts of laws rules) and, to the extent
applicable, federal law.

    (g) The 2001 Plan was originally effective on May 15, 2001. No Options may
be granted under the 2001 Plan after May 14, 2011; however, all previous Options
issued that have not expired under their original terms or will not then expire
at the time the 2001 Plan expires will remain outstanding.

    (h) Restrictions on Issuance of Shares

        (1) The Company shall not be obligated to sell or issue any Shares upon
    the exercise of any Option granted under the 2001 Plan unless: (i) the
    shares pertaining to such Option have been registered under applicable
    federal and state securities laws or are exempt from such registration; (ii)
    the prior approval of such sale or issuance has been obtained from any state
    regulatory body having jurisdiction; and (iii) in the event the Common Stock
    has been listed on any exchange, the shares pertaining to such Option have
    been duly listed on such exchange in accordance with the procedure specified
    therefor. The Company shall be under no obligation to effect or obtain any
    listing, registration, qualification, consent or approval with respect to
    shares pertaining to any Option granted under the 2001 Plan. If the shares
    to be issued upon the exercise of any Option granted under the 2001 Plan are
    intended to be issued by the Company in reliance upon the exemptions from
    the registration requirements of applicable federal and state securities
    laws, the recipient of the Option, if so requested by the Company, shall
    furnish to the Company such evidence and representations, including an
    opinion of counsel, satisfactory to it, as the Company may reasonably
    request.

        (2) The Company shall not be liable for damages due to a delay in the
    delivery or issuance of any stock certificates for any reason whatsoever,
    including, but not limited to, a delay caused by listing, registration or
    qualification of the shares of Common Stock pertaining to any Option granted
    under the 2001 Plan upon any securities exchange or under any federal or
    state law or the effecting or obtaining of any consent or approval of any
    governmental body.

    (i) The Board of Directors or Committee may impose such other restrictions
on the ownership and transfer of shares issued pursuant to the 2001 Plan as it
deems desirable; any such restrictions shall be set forth in the applicable
agreement.

    (j) The Board of Directors may amend, abandon, suspend or terminate the 2001
Plan or any portion thereof at any time in such respects as it may deem
advisable in its sole discretion, provided that no amendment shall be made
without stockholder approval (including an increase in the maximum number of
shares of Common Stock in respect of which Options may be made under the 2001
Plan) if such


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stockholder approval is necessary to comply with any tax or regulatory
requirement or exchange listing rules, including for these purposes any approval
requirement that is a prerequisite for exemptive relief under Section 16(b) of
the Exchange Act.

    (k) To preserve an Optionee's rights under an Option in the event of a
change in control of the Company or an Optionee's separation from employment,
the Committee in its discretion may, at the time an Option is made or any time
thereafter, take one or more of the following actions: (i) provide for the
acceleration of any time period relating to the exercise of the Option, (ii)
provide for the purchase of the Option, upon the Optionee's request, for an
amount of cash or other property that could have been received upon the exercise
or realization of the Option had the Option been currently exercisable or
payable, (iii) adjust the terms of the Option in a manner determined by the
Committee to reflect the change in control or to prevent the imposition of an
excise tax under section 280G(b) of the Code, (iv) cause the Option to be
assumed, or new rights substituted therefor, by another entity, or (v) make such
other provision as the Committee may consider equitable and in the best
interests of the Company.

AMENDED AND RESTATED as of May 6, 2003.

                                    ZIX CORPORATION




                                    By: /s/ RONALD A. WOESSNER
                                        ---------------------------------------
                                        Title: S.V.P.