EXHIBIT 99.1

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NEWS RELEASE                                               FOR IMMEDIATE RELEASE

                                                                     Page 1 of 2

ZIX CORPORATION RESTRUCTURES CONVERTIBLE NOTES

DALLAS -- APRIL 13, 2005 -- Zix Corporation (ZixCorp(R)), (Nasdaq: ZIXI), a
global provider of secure e-messaging, e-prescribing, and e-transaction
applications and services, today announced that it has entered into definitive
agreements with the holders of its $20 million convertible notes (due 2005 -
2008 as originally issued by the company in November 2004). These definitive
agreements relate to the previously announced changes to certain terms of the
convertible notes and related warrants.

As amended, the company will redeem $5 million principal amount of the notes by
July 31, 2005, (originally due November 2005) and $5 million principal amount by
December 31, 2005 (originally due November 2008) using the company's common
stock. Previously, the company could only repay the debt with the company's
common stock if the stock price was at or above $6 per share. The number of
shares to be issued will be determined by the volume weighted average price of
the common stock over fifteen days before each redemption, with limitations
based on trading volume of the common stock. If the company is unable to
complete redemption of these amounts by the scheduled dates, the company is
required to repay the balance of these principal installments in cash and issue
additional warrants to the noteholders in accordance with the original terms of
the notes. The 2006 and 2007 repayment dates remain unchanged.

Following completion of applicable securities laws filings, the amount, timing,
and frequency of the redemptions are entirely at the company's discretion and
the company can commence the redemption for stock at any time. The actual number
of common stock shares issued to redeem this initial $10 million principal
portion of the notes will depend on the market price of the company's common
stock at the time of redemption. Because of limitations imposed by Nasdaq rules,
the company may not issue more than approximately 6.2 million shares of its
common stock shares in connection with the conversion of the notes, payment of
the principal or redemption of the principal amount of the notes, and the
payment of interest on the notes and the exercise of the warrants originally
issued to the notes holders.

Also, the warrants originally issued to the notes holders, currently covering
1,000,000 company common shares at an exercise price of $6.00 per share, will be
amended, such that the exercise price for a pro-rata portion of the warrants
will be reduced to the price of the company's common shares as and when the $10
million of notes principal is redeemed.

                                     -more-

www.zixcorp.com 27 N. Haskell Ave. | Suite 2300, LB 36 | Dallas, TX 75204 |
phone 214 370 2000 | fax 214 370 2070



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Zix Corporation Restructures Convertible Notes                       Page 2 of 2

GENERAL TERMS

As before the amendments, the notes are secured by cash held in a segregated
account, whereby fifty percent of the principal amount owing under the notes is
required to be held in the segregated account. Pursuant to the amendments of the
notes, once the company has redeemed $10 million of the notes principal by
December 31, 2005, a note covenant that would have required the company to
maintain until November 2007 cash balances of $10 million (inclusive of the
amounts in the segregated account), will be relaxed such that the company will
be required to maintain cash and equivalents of $9 million. The required cash
balances will further decrease to $5 million in November 2006 concurrent with
the payment or retirement of the $5 million principal amount of the note due
November 2006.

The company's right to force conversion of any outstanding notes if the
company's common stock trades above $11.00 for specified periods and to force
the exercise of the warrants if the company's common stock trades above $15.00
for specified periods remains unchanged.

The amendments are not yet effective and are subject to various customary
closing conditions and to matters relating to SEC registration of the shares
that may be issued in the share redemptions. The company will file a Form 8-K
with the SEC by April 14, 2005, relating to this transaction, which will include
copies of the definitive amendment documents.

ABOUT ZIX CORPORATION

Zix Corporation (ZixCorp(R)) provides easy-to-use-and-deploy e-communication
services that protect, manage, and deliver sensitive information to enterprises
and consumers in healthcare, finance, insurance, and government. ZixCorp's
eSecure services enable policy-driven email encryption, content filtering and
send-to-anyone capability while its eHealth services improve patient care,
reduce costs, and improve efficiency through e-prescribing and e-lab solutions.
For more information, visit www.zixcorp.com.

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ZIXCORP CONTACTS:

Public Relations: Christa Osswald (214) 370-2175, publicrelations@zixcorp.com
Investor Relations: Peter Wilensky (214) 515-7357, invest@zixcorp.com

www.zixcorp.com 27 N. Haskell Ave. | Suite 2300, LB 36 | Dallas, TX 75204 |
phone 214 370 2000 | fax 214 370 2070