diff --git a/no-sse.diff b/no-sse.diff
new file mode 100644
index 0000000..f5707a6
--- /dev/null
+++ b/no-sse.diff
@@ -0,0 +1,24 @@
+---
+ configure.ac |    2 ++
+ 1 file changed, 2 insertions(+)
+
+Index: spandsp-3.0.0.g15/configure.ac
+===================================================================
+--- spandsp-3.0.0.g15.orig/configure.ac
++++ spandsp-3.0.0.g15/configure.ac
+@@ -350,6 +350,7 @@ gnu)
+     if test x"$ac_cv_gcc_unused_but_set_variable" = xyes ; then
+         COMP_VENDOR_CFLAGS="-Wunused-but-set-variable $COMP_VENDOR_CFLAGS"
+     fi
++if false; then
+     AX_CHECK_ARM_NEON([$host],
+         [AC_DEFINE([SPANDSP_USE_ARM_NEON], [1], [Use the ARM NEON instruction set])])
+     if test "$enable_neon" = "yes" ; then
+@@ -382,6 +383,7 @@ gnu)
+     if test "$enable_mmx" = "yes" ; then
+         COMP_VENDOR_CFLAGS="-mmmx $COMP_VENDOR_CFLAGS"
+     fi
++fi
+     case $host_os in
+     cygwin*)
+         COMP_VENDOR_LDFLAGS="-no-undefined"
diff --git a/spandsp.changes b/spandsp.changes
index 007f5b6..e2a0631 100644
--- a/spandsp.changes
+++ b/spandsp.changes
@@ -1,3 +1,8 @@
+-------------------------------------------------------------------
+Mon Apr 18 07:38:15 UTC 2022 - Jan Engelhardt <jengelh@inai.de>
+
+- Add no-sse.diff
+
 -------------------------------------------------------------------
 Sat Apr  2 07:34:40 UTC 2022 - Jan Engelhardt <jengelh@inai.de>
 
diff --git a/spandsp.spec b/spandsp.spec
index 06b0a9d..7d6827e 100644
--- a/spandsp.spec
+++ b/spandsp.spec
@@ -27,6 +27,7 @@ URL:            https://github.com/freeswitch/spandsp
 
 Source:         %name-%version.tar.xz
 Source2:        baselibs.conf
+Patch1:         no-sse.diff
 Patch2:         spandsp-raise-traintime-tolerance.diff
 Patch3:         spandsp-handle-international-dialstring-prefix.diff
 BuildRequires:  docbook-xsl-stylesheets
@@ -90,18 +91,14 @@ This package contains documentation for the libspandsp API.
 
 %prep
 %autosetup -p1
+# The cpuid calls in the source code only apply to a test program.
+# The library itself is (was) statically enabling -msse during configure, which
+# is now removed.
 
 %build
 %define _lto_cflags %nil
 autoreconf -fiv
-# Enabling MMX could be safe.. I see cpuid calls in the source
 %configure \
-%ifarch i586 i686
-	--enable-mmx \
-%endif
-%ifarch x86_64
-	--enable-sse --enable-sse2 \
-%endif
 	--disable-static \
 	--enable-doc
 %make_build