diff --git a/fix-i686-build.patch b/fix-i686-build.patch
new file mode 100644
index 0000000..bf38049
--- /dev/null
+++ b/fix-i686-build.patch
@@ -0,0 +1,90 @@
+From cf685defcd0c0026fce7ef1fc3fb79a1f1a1edaa Mon Sep 17 00:00:00 2001
+From: Sebastian Wick <sebastian.wick@redhat.com>
+Date: Mon, 8 Jan 2024 15:52:09 +0100
+Subject: [PATCH 1/2] cogl/half-float: Include SSE intrinsics
+
+The intel intrinsics (including SSE) are only included in the header if
+the arch is x86_64 which made the i686 build fail.
+
+Closes: https://gitlab.gnome.org/GNOME/mutter/-/issues/3234
+Fixes: 568506ecb ("cogl: Add half float implementation")
+---
+ cogl/cogl/cogl-half-float.c | 8 ++++++++
+ 1 file changed, 8 insertions(+)
+
+diff --git a/cogl/cogl/cogl-half-float.c b/cogl/cogl/cogl-half-float.c
+index be2c48b815..ae0af0a6a2 100644
+--- a/cogl/cogl/cogl-half-float.c
++++ b/cogl/cogl/cogl-half-float.c
+@@ -31,6 +31,13 @@
+ 
+ #include <math.h>
+ 
++#if defined(__SSE__) || \
++    (defined(_M_IX86_FP) && (_M_IX86_FP >= 1)) || \
++    (defined(_M_X64) && !defined(_M_ARM64EC))
++#include <xmmintrin.h>
++#include <emmintrin.h>
++#endif
++
+ #include "cogl/cogl-half-float.h"
+ #include "cogl/cogl-soft-float.h"
+ 
+@@ -262,3 +269,4 @@ uint16_t cogl_uint16_div_64k_to_half (uint16_t v)
+ 
+   return (e << 10) | m;
+ }
++
+-- 
+2.43.0
+
+
+From 0096860d715e1842d755b1229b43e848c26fb0cb Mon Sep 17 00:00:00 2001
+From: Sebastian Wick <sebastian.wick@redhat.com>
+Date: Mon, 8 Jan 2024 16:08:37 +0100
+Subject: [PATCH 2/2] cogl/bitmap-conversion: Don't break strict-aliasing for
+ flt_pack/unpack
+
+Simply reinterpreting the bytes differently is a strict-aliasing
+violation if the type of the object isn't char or the target type of the
+reinterpretation. None of that is the case here, so we have to resort to
+a memcpy.
+
+Fixes: 60c082caa ("cogl/bitmap-conversion: Support packing fp16 formats")
+---
+ cogl/cogl/cogl-bitmap-conversion.c | 11 +++++++++--
+ 1 file changed, 9 insertions(+), 2 deletions(-)
+
+diff --git a/cogl/cogl/cogl-bitmap-conversion.c b/cogl/cogl/cogl-bitmap-conversion.c
+index 76efbb9bb9..08ecce6a4d 100644
+--- a/cogl/cogl/cogl-bitmap-conversion.c
++++ b/cogl/cogl/cogl-bitmap-conversion.c
+@@ -45,16 +45,23 @@ typedef enum
+   MEDIUM_TYPE_FLOAT,
+ } MediumType;
+ 
++_Static_assert (sizeof (uint32_t) == sizeof (GLfloat),
++                "GLfloat doesn't have a size of 4 bytes");
++
+ inline static uint32_t
+ pack_flt (GLfloat b)
+ {
+-  return *(uint32_t *) &b;
++  uint32_t ret;
++  memcpy (&ret, &b, sizeof (uint32_t));
++  return ret;
+ }
+ 
+ inline static GLfloat
+ unpack_flt (uint32_t b)
+ {
+-  return *(GLfloat *) &b;
++  GLfloat ret;
++  memcpy (&ret, &b, sizeof (GLfloat));
++  return ret;
+ }
+ 
+ #define CLAMP_NORM(b) (MAX (MIN ((b), 1.0), 0.0))
+-- 
+2.43.0
+
diff --git a/mutter.spec b/mutter.spec
index 1580c0b..d9b18a6 100644
--- a/mutter.spec
+++ b/mutter.spec
@@ -44,6 +44,8 @@ Patch:         0001-Revert-x11-Use-input-region-from-frame-window-for-de.patch
 # which solves the problems reported with #3329 alone
 Patch: 0001-modified-3329.patch
 
+Patch: fix-i686-build.patch
+
 BuildRequires: pkgconfig(gobject-introspection-1.0) >= 1.41.0
 BuildRequires: pkgconfig(sm)
 BuildRequires: pkgconfig(libwacom)