diff --git a/C4/Letters.pm b/C4/Letters.pm
index ff17637ef6..f871c34503 100644
--- a/C4/Letters.pm
+++ b/C4/Letters.pm
@@ -1032,6 +1032,7 @@ sub EnqueueLetter {
         message_id => $id,
         borrowernumber => $who_letter_is_for,
         letter_code => $letter_code, # can be scalar or arrayref
+        exclude_letter_code => $exclude_letter_code, # can be scalar or arrayref
         type => $type, # can be scalar or arrayref
         limit => 50,
         verbose => 1,
@@ -1044,6 +1045,10 @@ The (optional) message_id, borrowernumber, letter_code, type and where
 parameter are used to select which pending messages will be processed. The
 limit parameter determines the volume of results, i.e. sent messages.
 
+The optional exclude_letter_code parameter processes all pending messages
+except those with the given letter code(s). It cannot be combined with
+letter_code; passing both raises a Koha::Exceptions::BadParameter exception.
+
 The optional verbose parameter can be used to generate debugging output.
 
 Returns number of messages sent.
@@ -1058,6 +1063,18 @@ sub SendQueuedMessages {
     Koha::Exceptions::BadParameter->throw("Parameter message_id cannot be empty if passed.")
         if ( exists( $params->{message_id} ) && !$params->{message_id} );
 
+    my $has_letter_code =
+        ref( $params->{letter_code} ) ? scalar @{ $params->{letter_code} } : $params->{letter_code};
+    my $has_exclude_letter_code =
+        ref( $params->{exclude_letter_code} )
+        ? scalar @{ $params->{exclude_letter_code} }
+        : $params->{exclude_letter_code};
+
+    # letter_code and exclude_letter_code build the same search key ('letter_code'); passing both
+    # would let one silently clobber the other in the hash literal built below.
+    Koha::Exceptions::BadParameter->throw("Parameters letter_code and exclude_letter_code are mutually exclusive.")
+        if ( $has_letter_code && $has_exclude_letter_code );
+
     if ( C4::Context->config("enable_plugins") ) {
         my @plugins = Koha::Plugins->new->GetPlugins(
             {
@@ -1084,16 +1101,16 @@ sub SendQueuedMessages {
             $params->{message_id}     ? ( message_id     => $params->{message_id} )     : (),
             $params->{borrowernumber} ? ( borrowernumber => $params->{borrowernumber} ) : (),
 
-            # Check for scalar or array in letter_code and type
-            ref( $params->{letter_code} )
-                && @{ $params->{letter_code} } ? ( letter_code => $params->{letter_code} ) : (),
-            !ref( $params->{letter_code} ) && $params->{letter_code} ? ( letter_code => $params->{letter_code} ) : (),
-
-            # Check for scalar or array in exclude_letter_code
-            ref( $params->{exclude_letter_code} )
-                && @{ $params->{exclude_letter_code} } ? ( letter_code => { '-not_in' => $params->{exclude_letter_code} } ) : (),
-            !ref( $params->{exclude_letter_code} )
-                && $params->{exclude_letter_code} ? ( letter_code => { '!=' => $params->{exclude_letter_code} } ) : (),
+            # letter_code and exclude_letter_code can each be scalar or arrayref; guaranteed
+            # mutually exclusive above, so they never both contribute a letter_code key here.
+            $has_letter_code ? ( letter_code => $params->{letter_code} ) : (),
+            $has_exclude_letter_code
+            ? (
+                letter_code => ref( $params->{exclude_letter_code} )
+                ? { '-not_in' => $params->{exclude_letter_code} }
+                : { '!='      => $params->{exclude_letter_code} }
+                )
+            : (),
 
             ref( $params->{type} )
                 && @{ $params->{type} }
diff --git a/misc/cronjobs/process_message_queue.pl b/misc/cronjobs/process_message_queue.pl
index 3d5ca291be..f28b1c81bc 100755
--- a/misc/cronjobs/process_message_queue.pl
+++ b/misc/cronjobs/process_message_queue.pl
@@ -75,6 +75,12 @@ ENDUSAGE
 
 die $usage if $help;
 
+# Remove empty elements, see bug 37075. -c/-x take an optional value ('c|code:s'), so a bare
+# flag with no value still leaves an empty string in the array; strip those before the
+# mutual-exclusivity check below, otherwise a bare -c would falsely trigger it (bug 40934).
+@letter_code         = grep { $_ ne q{} } @letter_code;
+@exclude_letter_code = grep { $_ ne q{} } @exclude_letter_code;
+
 if ( @letter_code && @exclude_letter_code ) {
     die "The options --code and --exclude-code are mutually exclusive.\nUse one or the other.\n" . $usage;
 }
@@ -91,10 +97,6 @@ try {
     exit;
 };
 
-# Remove empty elements, see bug 37075
-@letter_code         = grep { $_ ne q{} } @letter_code;
-@exclude_letter_code = grep { $_ ne q{} } @exclude_letter_code;
-
 C4::Letters::SendQueuedMessages(
     {
         verbose                => $verbose,
diff --git a/t/db_dependent/Letters.t b/t/db_dependent/Letters.t
index ec35595de1..f5946523cb 100755
--- a/t/db_dependent/Letters.t
+++ b/t/db_dependent/Letters.t
@@ -1826,7 +1826,7 @@ subtest 'Virtual method ->strftime in notices' => sub {
 };
 
 subtest 'Test exclude_letter_code parameter for SendQueuedMessages' => sub {
-    plan tests => 10;
+    plan tests => 12;
 
     my $dbh = C4::Context->dbh;
 
@@ -1947,6 +1947,34 @@ subtest 'Test exclude_letter_code parameter for SendQueuedMessages' => sub {
 
     is( Koha::Notice::Messages->find( $id[2] )->status, 'sent',    'ACQ_NOTIF message processed' );
     is( Koha::Notice::Messages->find( $id[3] )->status, 'pending', 'TEST_MESSAGE message excluded, still pending' );
+
+    # Reset messages to pending
+    Koha::Notice::Messages->find( $id[2] )->update( { status => 'pending' } );
+    Koha::Notice::Messages->find( $id[3] )->update( { status => 'pending' } );
+
+    throws_ok {
+        C4::Letters::SendQueuedMessages(
+            {
+                letter_code         => ['ACQ_NOTIF'],
+                exclude_letter_code => ['DUEDGST'],
+                type                => 'sms',
+            }
+        );
+    }
+    'Koha::Exceptions::BadParameter',
+        'SendQueuedMessages dies when letter_code and exclude_letter_code are both passed';
+
+    throws_ok {
+        C4::Letters::SendQueuedMessages(
+            {
+                letter_code         => 'ACQ_NOTIF',
+                exclude_letter_code => 'DUEDGST',
+                type                => 'sms',
+            }
+        );
+    }
+    'Koha::Exceptions::BadParameter',
+        'SendQueuedMessages dies when scalar letter_code and exclude_letter_code are both passed';
 };
 
 $schema->storage->txn_rollback;
diff --git a/t/db_dependent/cronjobs/process_message_queue.pl.t b/t/db_dependent/cronjobs/process_message_queue.pl.t
new file mode 100755
index 0000000000..6498d6c7a5
--- /dev/null
+++ b/t/db_dependent/cronjobs/process_message_queue.pl.t
@@ -0,0 +1,45 @@
+#!/usr/bin/perl
+#
+# This file is part of Koha.
+#
+# Koha is free software; you can redistribute it and/or modify it
+# under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 3 of the License, or
+# (at your option) any later version.
+#
+# Koha is distributed in the hope that it will be useful, but
+# WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with Koha; if not, see <https://www.gnu.org/licenses>.
+
+use Modern::Perl;
+
+use FindBin qw($Bin);
+use Test::More tests => 3;
+use Test::NoWarnings;
+
+# Regression tests for bug 40934: the --code/--exclude-code mutual-exclusivity
+# check must only fire when both options are given an actual value, not when
+# one is passed bare (GetOptions' optional-value ':s' type leaves an empty
+# string in the array in that case).
+
+my $script = "$Bin/../../../misc/cronjobs/process_message_queue.pl";
+
+# --where "1=0" keeps this a safe no-op: no message ever matches, so nothing
+# is ever sent even though the script runs for real against the test database.
+my $safe_run = "$^X $script --where '1=0'";
+
+my $output = `$safe_run --code FOO --exclude-code BAR 2>&1`;
+like(
+    $output, qr/mutually exclusive/i,
+    '--code and --exclude-code together are still rejected as mutually exclusive'
+);
+
+$output = `$safe_run -c --exclude-code DUEDGST 2>&1`;
+unlike(
+    $output, qr/mutually exclusive/i,
+    'bare -c with --exclude-code is not falsely rejected as mutually exclusive (bug 40934)'
+);