diff --git a/libs/vkd3d-shader/dxil.c b/libs/vkd3d-shader/dxil.c
index 54b7eefed..764cd25a1 100644
--- a/libs/vkd3d-shader/dxil.c
+++ b/libs/vkd3d-shader/dxil.c
@@ -2272,8 +2272,13 @@ static inline bool sm6_value_is_constant(const struct sm6_value *value)
 
 static bool sm6_value_is_constant_zero(const struct sm6_value *value)
 {
-    /* Constant vectors do not occur. */
-    return sm6_value_is_register(value) && register_is_scalar_constant_zero(&value->reg);
+    if (value->value_type != VALUE_TYPE_CONSTANT || value->type->class != TYPE_CLASS_INTEGER)
+        return false;
+
+    if (value->type->u.width == 64)
+        return value->u.constant.immconst.immconst_u64[0] == 0;
+    else
+        return value->u.constant.immconst.immconst_u32[0] == 0;
 }
 
 static inline bool sm6_value_is_undef(const struct sm6_value *value)
diff --git a/libs/vkd3d-shader/vkd3d_shader_private.h b/libs/vkd3d-shader/vkd3d_shader_private.h
index c29ec28a9..7620dbfcb 100644
--- a/libs/vkd3d-shader/vkd3d_shader_private.h
+++ b/libs/vkd3d-shader/vkd3d_shader_private.h
@@ -1337,12 +1337,6 @@ static inline bool register_is_constant_or_undef(const struct vkd3d_shader_regis
     return register_is_constant(reg) || register_is_undef(reg);
 }
 
-static inline bool register_is_scalar_constant_zero(const struct vkd3d_shader_register *reg)
-{
-    return register_is_constant(reg) && reg->dimension == VSIR_DIMENSION_SCALAR
-            && (data_type_is_64_bit(reg->data_type) ? !reg->u.immconst_u64[0] : !reg->u.immconst_u32[0]);
-}
-
 static inline bool register_is_numeric_array(const struct vkd3d_shader_register *reg)
 {
     return (reg->type == VKD3DSPR_IMMCONSTBUFFER || reg->type == VKD3DSPR_IDXTEMP