diff --git a/src/gallium/drivers/llvmpipe/lp_texture.c b/src/gallium/drivers/llvmpipe/lp_texture.c
index c65a4bc5fae..1335b1ed9c4 100644
--- a/src/gallium/drivers/llvmpipe/lp_texture.c
+++ b/src/gallium/drivers/llvmpipe/lp_texture.c
@@ -852,10 +852,12 @@ static bool llvmpipe_resource_bind_backing(struct pipe_screen *screen,
    if (!lpr->backable)
       return FALSE;
 
+   if (llvmpipe_resource_is_texture(&lpr->base)) {
+      if (lpr->size_required > LP_MAX_TEXTURE_SIZE)
+         return FALSE;
 
-   if (llvmpipe_resource_is_texture(&lpr->base))
       lpr->tex_data = (char *)pmem + offset;
-   else
+   } else
       lpr->data = (char *)pmem + offset;
    lpr->backing_offset = offset;
 
diff --git a/src/gallium/frontends/lavapipe/lvp_device.c b/src/gallium/frontends/lavapipe/lvp_device.c
index a153c190ad8..846abcd110d 100644
--- a/src/gallium/frontends/lavapipe/lvp_device.c
+++ b/src/gallium/frontends/lavapipe/lvp_device.c
@@ -1629,12 +1629,18 @@ VKAPI_ATTR VkResult VKAPI_CALL lvp_BindImageMemory2(VkDevice _device,
       }
 
       if (!did_bind) {
+         if (!device->pscreen->resource_bind_backing(device->pscreen,
+                                                     image->bo,
+                                                     mem->pmem,
+                                                     bind_info->memoryOffset)) {
+            /* This is probably caused by the texture being too large, so let's
+             * report this as the *closest* allowed error-code. It's not ideal,
+             * but it's unlikely that anyone will care too much.
+             */
+            return vk_error(device->instance, VK_ERROR_OUT_OF_DEVICE_MEMORY);
+         }
          image->pmem = mem->pmem;
          image->memory_offset = bind_info->memoryOffset;
-         device->pscreen->resource_bind_backing(device->pscreen,
-                                                image->bo,
-                                                mem->pmem,
-                                                bind_info->memoryOffset);
       }
    }
    return VK_SUCCESS;