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Private legal tender

A simpler variation on what was suggested would go like this:

Customer sends cash or money order to digital bank, along with a floppy
with an anonymous email address (via a remailer) and a public key.  The
bank emails the customer encrypted digital cash corresponding to the
amount he sent in (minus any service charges).  If Chaum blinding is
used, the needed data can be included on the floppy.  Alternatives to
sending a floppy would be for the customer to email the same information
when he mailed his money, including some secret information with both
which would tie them together.

Customers spend money using the appropriate protocols.

When a customer wants, he can send his digital cash to the bank to get
it exchanged for new digital cash; or he can include with the digital
cash instructions to tell the bank to mail a check or money order to
a specified address.  Here is where he could use a postal mail drop if
he doesn't want to reveal his own identity (assuming he is mailing to
himself); or he may request mailing to some other business which doesn't
accept digital cash but from which he wants to purchase something.