diff --git a/src/cairo-gl-device.c b/src/cairo-gl-device.c
index 37c837d27..b6a9c15f3 100644
--- a/src/cairo-gl-device.c
+++ b/src/cairo-gl-device.c
@@ -112,6 +112,11 @@ _gl_finish (void *device)
     for (n = 0; n < ARRAY_LENGTH (ctx->glyph_cache); n++)
 	_cairo_gl_glyph_cache_fini (ctx, &ctx->glyph_cache[n]);
 
+    if (ctx->depth_stencil_info.id)
+	ctx->dispatch.DeleteRenderbuffers (1, &ctx->depth_stencil_info.id);
+    if (ctx->msaa_depth_stencil_info.id)
+	ctx->dispatch.DeleteRenderbuffers (1, &ctx->msaa_depth_stencil_info.id);
+
     _gl_unlock (device);
 }
 
@@ -453,36 +458,59 @@ _cairo_gl_ensure_multisampling (cairo_gl_context_t *ctx,
 }
 #endif
 
+static void
+_cairo_gl_replace_msaa_depth_stencil_buffer (cairo_gl_context_t *ctx,
+					     int width,
+					     int height)
+{
+    cairo_gl_dispatch_t *dispatch = &ctx->dispatch;
+
+    if (ctx->msaa_depth_stencil_info.id)
+	dispatch->DeleteRenderbuffers (1, &ctx->msaa_depth_stencil_info.id);
+
+    dispatch->GenRenderbuffers (1, &ctx->msaa_depth_stencil_info.id);
+    dispatch->BindRenderbuffer (GL_RENDERBUFFER, ctx->msaa_depth_stencil_info.id);
+    dispatch->RenderbufferStorageMultisample (GL_RENDERBUFFER, ctx->num_samples,
+					      _get_depth_stencil_format (ctx),
+					      width, height);
+    ctx->msaa_depth_stencil_info.width = width;
+    ctx->msaa_depth_stencil_info.height = height;
+    ctx->msaa_depth_stencil_info.surfaces_with_same_size = 0;
+}
+
 static cairo_bool_t
 _cairo_gl_ensure_msaa_depth_stencil_buffer (cairo_gl_context_t *ctx,
 					    cairo_gl_surface_t *surface)
 {
     cairo_gl_dispatch_t *dispatch = &ctx->dispatch;
-    if (surface->msaa_depth_stencil)
-	return TRUE;
-
     _cairo_gl_ensure_framebuffer (ctx, surface);
 #if CAIRO_HAS_GL_SURFACE
     if (ctx->gl_flavor == CAIRO_GL_FLAVOR_DESKTOP)
 	_cairo_gl_ensure_multisampling (ctx, surface);
 #endif
 
-    dispatch->GenRenderbuffers (1, &surface->msaa_depth_stencil);
-    dispatch->BindRenderbuffer (GL_RENDERBUFFER,
-			        surface->msaa_depth_stencil);
+    if (! ctx->msaa_depth_stencil_info.id ||
+        ctx->msaa_depth_stencil_info.width < surface->width ||
+        ctx->msaa_depth_stencil_info.height < surface->height) {
+	_cairo_gl_replace_msaa_depth_stencil_buffer (ctx,
+						     surface->width,
+						     surface->height);
+    }
 
-    dispatch->RenderbufferStorageMultisample (GL_RENDERBUFFER,
-					      ctx->num_samples,
-					      _get_depth_stencil_format (ctx),
-					      surface->width,
-					      surface->height);
+    assert (ctx->msaa_depth_stencil_info.id);
+    if (surface->msaa_depth_stencil == ctx->msaa_depth_stencil_info.id)
+	return TRUE;
+
+    if (ctx->msaa_depth_stencil_info.width == surface->width &&
+	ctx->msaa_depth_stencil_info.height == surface->height)
+    ctx->msaa_depth_stencil_info.surfaces_with_same_size++;
 
 #if CAIRO_HAS_GL_SURFACE
     if (ctx->gl_flavor == CAIRO_GL_FLAVOR_DESKTOP) {
 	dispatch->FramebufferRenderbuffer (GL_FRAMEBUFFER,
 					   GL_DEPTH_STENCIL_ATTACHMENT,
 					   GL_RENDERBUFFER,
-					   surface->msaa_depth_stencil);
+					   ctx->msaa_depth_stencil_info.id);
     }
 #endif
 
@@ -491,50 +519,72 @@ _cairo_gl_ensure_msaa_depth_stencil_buffer (cairo_gl_context_t *ctx,
 	dispatch->FramebufferRenderbuffer (GL_FRAMEBUFFER,
 					   GL_DEPTH_ATTACHMENT,
 					   GL_RENDERBUFFER,
-					   surface->msaa_depth_stencil);
+					   ctx->msaa_depth_stencil_info.id);
 	dispatch->FramebufferRenderbuffer (GL_FRAMEBUFFER,
 					   GL_STENCIL_ATTACHMENT,
 					   GL_RENDERBUFFER,
-					   surface->msaa_depth_stencil);
+					   ctx->msaa_depth_stencil_info.id);
     }
 #endif
 
-    if (dispatch->CheckFramebufferStatus (GL_FRAMEBUFFER) != GL_FRAMEBUFFER_COMPLETE) {
-	dispatch->DeleteRenderbuffers (1, &surface->msaa_depth_stencil);
-	surface->msaa_depth_stencil = 0;
-	return FALSE;
-    }
+    surface->msaa_depth_stencil = ctx->msaa_depth_stencil_info.id;
 
+    if (dispatch->CheckFramebufferStatus (GL_FRAMEBUFFER) != GL_FRAMEBUFFER_COMPLETE)
+	return FALSE;
     return TRUE;
 }
 
+static void
+_cairo_gl_replace_depth_stencil_buffer (cairo_gl_context_t *ctx,
+					int width,
+					int height)
+{
+    cairo_gl_dispatch_t *dispatch = &ctx->dispatch;
+
+    if (ctx->depth_stencil_info.id)
+	dispatch->DeleteRenderbuffers (1, &ctx->depth_stencil_info.id);
+
+    dispatch->GenRenderbuffers (1, &ctx->depth_stencil_info.id);
+    dispatch->BindRenderbuffer (GL_RENDERBUFFER, ctx->depth_stencil_info.id);
+    dispatch->RenderbufferStorage (GL_RENDERBUFFER,
+				   _get_depth_stencil_format (ctx),
+				   width, height);
+    ctx->depth_stencil_info.width = width;
+    ctx->depth_stencil_info.height = height;
+    ctx->depth_stencil_info.surfaces_with_same_size = 0;
+}
+
 static cairo_bool_t
 _cairo_gl_ensure_depth_stencil_buffer (cairo_gl_context_t *ctx,
 				       cairo_gl_surface_t *surface)
 {
     cairo_gl_dispatch_t *dispatch = &ctx->dispatch;
 
-    if (surface->depth_stencil)
-	return TRUE;
-
     _cairo_gl_ensure_framebuffer (ctx, surface);
 
-    dispatch->GenRenderbuffers (1, &surface->depth_stencil);
-    dispatch->BindRenderbuffer (GL_RENDERBUFFER, surface->depth_stencil);
-    dispatch->RenderbufferStorage (GL_RENDERBUFFER,
-				   _get_depth_stencil_format (ctx),
-				   surface->width, surface->height);
-
-    dispatch->FramebufferRenderbuffer (GL_FRAMEBUFFER, GL_STENCIL_ATTACHMENT,
-				       GL_RENDERBUFFER, surface->depth_stencil);
-    dispatch->FramebufferRenderbuffer (GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT,
-				       GL_RENDERBUFFER, surface->depth_stencil);
-    if (dispatch->CheckFramebufferStatus (GL_FRAMEBUFFER) != GL_FRAMEBUFFER_COMPLETE) {
-	dispatch->DeleteRenderbuffers (1, &surface->depth_stencil);
-	surface->depth_stencil = 0;
-	return FALSE;
+    if (! ctx->depth_stencil_info.id ||
+        ctx->depth_stencil_info.width < surface->width ||
+        ctx->depth_stencil_info.height < surface->height) {
+	_cairo_gl_replace_depth_stencil_buffer (ctx,
+						surface->width,
+						surface->height);
     }
 
+    if (surface->depth_stencil == ctx->depth_stencil_info.id)
+	return TRUE;
+
+    if (ctx->depth_stencil_info.width == surface->width &&
+	ctx->depth_stencil_info.height == surface->height)
+    ctx->depth_stencil_info.surfaces_with_same_size++;
+
+    dispatch->FramebufferRenderbuffer (GL_FRAMEBUFFER, GL_STENCIL_ATTACHMENT,
+				       GL_RENDERBUFFER, ctx->depth_stencil_info.id);
+    dispatch->FramebufferRenderbuffer (GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT,
+				       GL_RENDERBUFFER, ctx->depth_stencil_info.id);
+    surface->depth_stencil = ctx->depth_stencil_info.id;
+
+    if (dispatch->CheckFramebufferStatus (GL_FRAMEBUFFER) != GL_FRAMEBUFFER_COMPLETE)
+	return FALSE;
     return TRUE;
 }
 
diff --git a/src/cairo-gl-private.h b/src/cairo-gl-private.h
index 7c97c49a6..088a87444 100644
--- a/src/cairo-gl-private.h
+++ b/src/cairo-gl-private.h
@@ -301,6 +301,13 @@ typedef struct _cairo_gl_dispatch {
 					     GLint level, GLsizei samples);
 } cairo_gl_dispatch_t;
 
+typedef struct _cairo_gl_shared_depth_stencil_info {
+    GLuint id;
+    int width;
+    int height;
+    unsigned surfaces_with_same_size;
+} cairo_gl_shared_depth_stencil_info_t;
+
 struct _cairo_gl_context {
     cairo_device_t base;
 
@@ -353,6 +360,12 @@ struct _cairo_gl_context {
 
     cairo_bool_t thread_aware;
 
+    /* GL stencil and depth buffers are shared among all surfaces
+       to preserve memory. In the future this could be a pool of renderbuffers
+       with an eviction policy. */
+    cairo_gl_shared_depth_stencil_info_t depth_stencil_info;
+    cairo_gl_shared_depth_stencil_info_t msaa_depth_stencil_info;
+
     void (*acquire) (void *ctx);
     void (*release) (void *ctx);
 
diff --git a/src/cairo-gl-surface.c b/src/cairo-gl-surface.c
index c0ee79f8a..7c9332270 100644
--- a/src/cairo-gl-surface.c
+++ b/src/cairo-gl-surface.c
@@ -946,6 +946,23 @@ static int _cairo_gl_surface_flavor (cairo_gl_surface_t *surface)
     return ctx->gl_flavor;
 }
 
+static void
+_cairo_gl_shrink_shared_renderbuffer (cairo_gl_context_t *ctx,
+				      cairo_gl_shared_depth_stencil_info_t *info,
+				      int surface_width,
+				      int surface_height)
+{
+    if (info->width != surface_width || info->height != surface_height)
+	return;
+
+    /* Force the creation of a new shared renderbuffer if we are the
+     * last surface that has the same size as our old shared buffer. */
+    ctx->dispatch.DeleteRenderbuffers (1, &info->id);
+    info->height = 0;
+    info->width = 0;
+    info->id = 0;
+}
+
 static cairo_status_t
 _cairo_gl_surface_finish (void *abstract_surface)
 {
@@ -968,18 +985,24 @@ _cairo_gl_surface_finish (void *abstract_surface)
 
     if (surface->fb)
         ctx->dispatch.DeleteFramebuffers (1, &surface->fb);
-    if (surface->depth_stencil)
-        ctx->dispatch.DeleteRenderbuffers (1, &surface->depth_stencil);
     if (surface->owns_tex)
 	glDeleteTextures (1, &surface->tex);
 
+    if (surface->depth_stencil) {
+	_cairo_gl_shrink_shared_renderbuffer (ctx, &ctx->depth_stencil_info,
+					      surface->width, surface->height);
+    }
+
 #if CAIRO_HAS_GL_SURFACE
-    if (surface->msaa_depth_stencil)
-	ctx->dispatch.DeleteRenderbuffers (1, &surface->msaa_depth_stencil);
     if (surface->msaa_fb)
 	ctx->dispatch.DeleteFramebuffers (1, &surface->msaa_fb);
     if (surface->msaa_rb)
 	ctx->dispatch.DeleteRenderbuffers (1, &surface->msaa_rb);
+
+    if (surface->msaa_depth_stencil) {
+	_cairo_gl_shrink_shared_renderbuffer (ctx, &ctx->msaa_depth_stencil_info,
+					      surface->width, surface->height);
+    }
 #endif
 
     return _cairo_gl_context_release (ctx, status);