diff --git a/cogl/cogl-blit.c b/cogl/cogl-blit.c
index ea457b958..fffd9ede6 100644
--- a/cogl/cogl-blit.c
+++ b/cogl/cogl-blit.c
@@ -51,7 +51,7 @@ _cogl_blit_texture_render_begin (CoglBlitData *data)
   unsigned int dst_width, dst_height;
   CoglError *ignore_error = NULL;
 
-  offscreen = _cogl_offscreen_new_to_texture_full
+  offscreen = _cogl_offscreen_new_with_texture_full
     (data->dst_tex, COGL_OFFSCREEN_DISABLE_DEPTH_AND_STENCIL, 0 /* level */);
 
   fb = COGL_FRAMEBUFFER (offscreen);
@@ -156,7 +156,7 @@ _cogl_blit_framebuffer_begin (CoglBlitData *data)
       !(ctx->private_feature_flags & COGL_PRIVATE_FEATURE_OFFSCREEN_BLIT))
     return FALSE;
 
-  dst_offscreen = _cogl_offscreen_new_to_texture_full
+  dst_offscreen = _cogl_offscreen_new_with_texture_full
     (data->dst_tex, COGL_OFFSCREEN_DISABLE_DEPTH_AND_STENCIL, 0 /* level */);
 
   dst_fb = COGL_FRAMEBUFFER (dst_offscreen);
@@ -166,7 +166,7 @@ _cogl_blit_framebuffer_begin (CoglBlitData *data)
       goto error;
     }
 
-  src_offscreen= _cogl_offscreen_new_to_texture_full
+  src_offscreen= _cogl_offscreen_new_with_texture_full
     (data->src_tex,
      COGL_OFFSCREEN_DISABLE_DEPTH_AND_STENCIL,
      0 /* level */);
@@ -227,7 +227,7 @@ _cogl_blit_copy_tex_sub_image_begin (CoglBlitData *data)
   if (!cogl_is_texture_2d (data->dst_tex))
     return FALSE;
 
-  offscreen = _cogl_offscreen_new_to_texture_full
+  offscreen = _cogl_offscreen_new_with_texture_full
     (data->src_tex, COGL_OFFSCREEN_DISABLE_DEPTH_AND_STENCIL, 0 /* level */);
 
   fb = COGL_FRAMEBUFFER (offscreen);
diff --git a/cogl/cogl-framebuffer-private.h b/cogl/cogl-framebuffer-private.h
index a220de9cf..233f1c521 100644
--- a/cogl/cogl-framebuffer-private.h
+++ b/cogl/cogl-framebuffer-private.h
@@ -56,7 +56,7 @@ typedef struct
   CoglBool depth_texture_enabled;
 } CoglFramebufferConfig;
 
-/* Flags to pass to _cogl_offscreen_new_to_texture_full */
+/* Flags to pass to _cogl_offscreen_new_with_texture_full */
 typedef enum
 {
   COGL_OFFSCREEN_DISABLE_DEPTH_AND_STENCIL = 1
@@ -209,7 +209,7 @@ struct _CoglOffscreen
 
   CoglOffscreenAllocateFlags allocation_flags;
 
-  /* FIXME: _cogl_offscreen_new_to_texture_full should be made to use
+  /* FIXME: _cogl_offscreen_new_with_texture_full should be made to use
    * fb->config to configure if we want a depth or stencil buffer so
    * we can get rid of these flags */
   CoglOffscreenFlags create_flags;
@@ -302,7 +302,7 @@ void
 _cogl_free_framebuffer_stack (GSList *stack);
 
 /*
- * _cogl_offscreen_new_to_texture_full:
+ * _cogl_offscreen_new_with_texture_full:
  * @texture: A #CoglTexture pointer
  * @create_flags: Flags specifying how to create the FBO
  * @level: The mipmap level within the texture to target
@@ -315,9 +315,9 @@ _cogl_free_framebuffer_stack (GSList *stack);
  * Return value: the new CoglOffscreen object.
  */
 CoglOffscreen *
-_cogl_offscreen_new_to_texture_full (CoglTexture *texture,
-                                     CoglOffscreenFlags create_flags,
-                                     int level);
+_cogl_offscreen_new_with_texture_full (CoglTexture *texture,
+                                       CoglOffscreenFlags create_flags,
+                                       int level);
 
 /*
  * _cogl_push_framebuffers:
diff --git a/cogl/cogl-framebuffer.c b/cogl/cogl-framebuffer.c
index fbd3dd6d7..8487578b1 100644
--- a/cogl/cogl-framebuffer.c
+++ b/cogl/cogl-framebuffer.c
@@ -607,9 +607,9 @@ _cogl_framebuffer_flush_dependency_journals (CoglFramebuffer *framebuffer)
 }
 
 CoglOffscreen *
-_cogl_offscreen_new_to_texture_full (CoglTexture *texture,
-                                     CoglOffscreenFlags create_flags,
-                                     int level)
+_cogl_offscreen_new_with_texture_full (CoglTexture *texture,
+                                       CoglOffscreenFlags create_flags,
+                                       int level)
 {
   CoglContext *ctx = texture->context;
   CoglOffscreen *offscreen;
@@ -617,7 +617,6 @@ _cogl_offscreen_new_to_texture_full (CoglTexture *texture,
   int level_width;
   int level_height;
   CoglOffscreen *ret;
-  CoglError *error = NULL;
 
   _COGL_RETURN_VAL_IF_FAIL (cogl_is_texture (texture), NULL);
   _COGL_RETURN_VAL_IF_FAIL (level < _cogl_texture_get_n_levels (texture),
@@ -649,9 +648,19 @@ _cogl_offscreen_new_to_texture_full (CoglTexture *texture,
 
   _cogl_texture_associate_framebuffer (texture, fb);
 
-  if (!cogl_framebuffer_allocate (ret, &error))
+  return ret;
+}
+
+/* XXX: deprecated api */
+CoglOffscreen *
+cogl_offscreen_new_to_texture (CoglTexture *texture)
+{
+  CoglOffscreen *ret = _cogl_offscreen_new_with_texture_full (texture, 0, 0);
+  CoglError *error = NULL;
+
+  if (!cogl_framebuffer_allocate (COGL_FRAMEBUFFER (ret), &error))
     {
-      cogl_object_unref (offscreen);
+      cogl_object_unref (ret);
       cogl_error_free (error);
       ret = NULL;
     }
@@ -660,9 +669,9 @@ _cogl_offscreen_new_to_texture_full (CoglTexture *texture,
 }
 
 CoglOffscreen *
-cogl_offscreen_new_to_texture (CoglTexture *texture)
+cogl_offscreen_new_with_texture (CoglTexture *texture)
 {
-  return _cogl_offscreen_new_to_texture_full (texture, 0, 0);
+  return _cogl_offscreen_new_with_texture_full (texture, 0, 0);
 }
 
 static void
diff --git a/cogl/cogl-framebuffer.h b/cogl/cogl-framebuffer.h
index b83d27969..554cc50bf 100644
--- a/cogl/cogl-framebuffer.h
+++ b/cogl/cogl-framebuffer.h
@@ -70,7 +70,7 @@ COGL_BEGIN_DECLS
  *
  * If you want to create a new framebuffer then you should start by
  * looking at the #CoglOnscreen and #CoglOffscreen constructor
- * functions, such as cogl_offscreen_new_to_texture() or
+ * functions, such as cogl_offscreen_new_with_texture() or
  * cogl_onscreen_new(). The #CoglFramebuffer interface deals with
  * all aspects that are common between those two types of framebuffer.
  *
@@ -795,7 +795,7 @@ cogl_framebuffer_set_color_mask (CoglFramebuffer *framebuffer,
  *
  * Queries the common #CoglPixelFormat of all color buffers attached
  * to this framebuffer. For an offscreen framebuffer created with
- * cogl_offscreen_new_to_texture() this will correspond to the format
+ * cogl_offscreen_new_with_texture() this will correspond to the format
  * of the texture.
  *
  * Since: 1.8
diff --git a/cogl/cogl-gles2-context.c b/cogl/cogl-gles2-context.c
index ade857007..43fa12d6d 100644
--- a/cogl/cogl-gles2-context.c
+++ b/cogl/cogl-gles2-context.c
@@ -330,7 +330,7 @@ copy_flipped_texture (CoglGLES2Context *gles2_ctx,
       CoglPipeline *pipeline = cogl_pipeline_new (ctx);
       const CoglOffscreenFlags flags = COGL_OFFSCREEN_DISABLE_DEPTH_AND_STENCIL;
       CoglOffscreen *offscreen =
-        _cogl_offscreen_new_to_texture_full (COGL_TEXTURE (dst_texture),
+        _cogl_offscreen_new_with_texture_full (COGL_TEXTURE (dst_texture),
                                              flags, level);
       int src_width = cogl_texture_get_width (src_texture);
       int src_height = cogl_texture_get_height (src_texture);
diff --git a/cogl/cogl-offscreen.h b/cogl/cogl-offscreen.h
index a97d9d7db..4449ad68f 100644
--- a/cogl/cogl-offscreen.h
+++ b/cogl/cogl-offscreen.h
@@ -47,6 +47,41 @@ typedef struct _CoglOffscreen CoglOffscreen;
 
 /* Offscreen api */
 
+/**
+ * cogl_offscreen_new_with_texture:
+ * @texture: A #CoglTexture pointer
+ *
+ * This creates an offscreen framebuffer object using the given
+ * @texture as the primary color buffer. It doesn't just initialize
+ * the contents of the offscreen buffer with the @texture; they are
+ * tightly bound so that drawing to the offscreen buffer effectively
+ * updates the contents of the given texture. You don't need to
+ * destroy the offscreen buffer before you can use the @texture again.
+ *
+ * <note>This api only works with low-level #CoglTexture types such as
+ * #CoglTexture2D, #CoglTexture3D and #CoglTextureRectangle, and not
+ * with meta-texture types such as #CoglTexture2DSliced.</note>
+ *
+ * The storage for the framebuffer is actually allocated lazily
+ * so this function will never return %NULL to indicate a runtime
+ * error. This means it is still possible to configure the framebuffer
+ * before it is really allocated.
+ *
+ * Simple applications without full error handling can simply rely on
+ * Cogl to lazily allocate the storage of framebuffers but you should
+ * be aware that if Cogl encounters an error (such as running out of
+ * GPU memory) then your application will simply abort with an error
+ * message. If you need to be able to catch such exceptions at runtime
+ * then you can explicitly allocate your framebuffer when you have
+ * finished configuring it by calling cogl_framebuffer_allocate() and
+ * passing in a #CoglError argument to catch any exceptions.
+ *
+ * Return value: (transfer full): a newly instantiated #CoglOffscreen
+ *   framebuffer.
+ */
+CoglOffscreen *
+cogl_offscreen_new_with_texture (CoglTexture *texture);
+
 /**
  * cogl_offscreen_new_to_texture:
  * @texture: A #CoglTexture pointer
@@ -65,9 +100,11 @@ typedef struct _CoglOffscreen CoglOffscreen;
  * Return value: (transfer full): a newly instantiated #CoglOffscreen
  *   framebuffer or %NULL if it wasn't possible to create the
  *   buffer.
+ * Deprecated: 1.16: Use cogl_offscreen_new_with_texture instead.
  */
 CoglOffscreen *
-cogl_offscreen_new_to_texture (CoglTexture *texture);
+cogl_offscreen_new_to_texture (CoglTexture *texture)
+    COGL_DEPRECATED_IN_1_16_FOR (cogl_offscreen_new_with_texture);
 
 /**
  * cogl_is_offscreen:
diff --git a/cogl/cogl-texture.c b/cogl/cogl-texture.c
index a616891c3..bb074dcce 100644
--- a/cogl/cogl-texture.c
+++ b/cogl/cogl-texture.c
@@ -854,7 +854,7 @@ get_texture_bits_via_offscreen (CoglTexture    *texture,
   if (!cogl_has_feature (ctx, COGL_FEATURE_ID_OFFSCREEN))
     return FALSE;
 
-  offscreen = _cogl_offscreen_new_to_texture_full
+  offscreen = _cogl_offscreen_new_with_texture_full
                                       (texture,
                                        COGL_OFFSCREEN_DISABLE_DEPTH_AND_STENCIL,
                                        0);
diff --git a/cogl/cogl.symbols b/cogl/cogl.symbols
index 0766c3170..8d1bdbea8 100644
--- a/cogl/cogl.symbols
+++ b/cogl/cogl.symbols
@@ -513,7 +513,7 @@ cogl_object_ref
 cogl_object_set_user_data
 cogl_object_unref
 
-cogl_offscreen_new_to_texture
+cogl_offscreen_new_with_texture
 
 cogl_onscreen_add_frame_callback
 cogl_onscreen_add_resize_handler
diff --git a/doc/reference/cogl-2.0-experimental/cogl-2.0-experimental-sections.txt b/doc/reference/cogl-2.0-experimental/cogl-2.0-experimental-sections.txt
index 6b2dfeccf..385a97a7f 100644
--- a/doc/reference/cogl-2.0-experimental/cogl-2.0-experimental-sections.txt
+++ b/doc/reference/cogl-2.0-experimental/cogl-2.0-experimental-sections.txt
@@ -650,7 +650,7 @@ CoglOffscreen
 cogl_is_offscreen
 
 <SUBSECTION>
-cogl_offscreen_new_to_texture
+cogl_offscreen_new_with_texture
 </SECTION>
 
 <SECTION>
diff --git a/doc/reference/cogl/cogl-sections.txt b/doc/reference/cogl/cogl-sections.txt
index 60c0048a4..bc19aa91c 100644
--- a/doc/reference/cogl/cogl-sections.txt
+++ b/doc/reference/cogl/cogl-sections.txt
@@ -267,6 +267,7 @@ cogl_program_set_uniform_matrix
 <SECTION>
 <FILE>cogl-offscreen</FILE>
 <TITLE>Offscreen Buffers</TITLE>
+cogl_offscreen_new_with_texture
 cogl_offscreen_new_to_texture
 cogl_is_offscreen
 cogl_set_framebuffer
diff --git a/examples/cogl-gles2-context.c b/examples/cogl-gles2-context.c
index f696dcae1..4f4fbfa93 100644
--- a/examples/cogl-gles2-context.c
+++ b/examples/cogl-gles2-context.c
@@ -100,7 +100,7 @@ main (int argc, char **argv)
                                      OFFSCREEN_WIDTH,
                                      OFFSCREEN_HEIGHT,
                                      COGL_PIXEL_FORMAT_ANY));
-    data.offscreen = cogl_offscreen_new_to_texture (data.offscreen_texture);
+    data.offscreen = cogl_offscreen_new_with_texture (data.offscreen_texture);
 
     data.gles2_ctx = cogl_gles2_context_new (data.ctx, &error);
     if (!data.gles2_ctx) {
diff --git a/examples/cogl-msaa.c b/examples/cogl-msaa.c
index b498c42cc..70b1a3d37 100644
--- a/examples/cogl-msaa.c
+++ b/examples/cogl-msaa.c
@@ -65,7 +65,7 @@ main (int argc, char **argv)
     tex = COGL_TEXTURE (cogl_texture_2d_new_with_size (ctx,
                                                        320, 480,
                                                        COGL_PIXEL_FORMAT_ANY));
-    offscreen = cogl_offscreen_new_to_texture (tex);
+    offscreen = cogl_offscreen_new_with_texture (tex);
     offscreen_fb = COGL_FRAMEBUFFER (offscreen);
     cogl_framebuffer_set_samples_per_pixel (offscreen_fb, 4);
     if (!cogl_framebuffer_allocate (offscreen_fb, &error))
diff --git a/test-fixtures/test-utils.c b/test-fixtures/test-utils.c
index e085beb36..174920137 100644
--- a/test-fixtures/test-utils.c
+++ b/test-fixtures/test-utils.c
@@ -179,7 +179,7 @@ test_utils_init (TestFlags requirement_flags,
       CoglTexture2D *tex = cogl_texture_2d_new_with_size (test_ctx,
                                                           FB_WIDTH, FB_HEIGHT,
                                                           COGL_PIXEL_FORMAT_ANY);
-      offscreen = cogl_offscreen_new_to_texture (COGL_TEXTURE (tex));
+      offscreen = cogl_offscreen_new_with_texture (COGL_TEXTURE (tex));
       test_fb = COGL_FRAMEBUFFER (offscreen);
     }
 
diff --git a/tests/conform/test-backface-culling.c b/tests/conform/test-backface-culling.c
index 8dc3e5736..e530e408c 100644
--- a/tests/conform/test-backface-culling.c
+++ b/tests/conform/test-backface-culling.c
@@ -298,7 +298,7 @@ test_backface_culling (void)
                                           TEST_UTILS_TEXTURE_NO_SLICING,
                                           COGL_PIXEL_FORMAT_ANY); /* internal
                                                                      format */
-  state.offscreen = COGL_FRAMEBUFFER (cogl_offscreen_new_to_texture (tex));
+  state.offscreen = COGL_FRAMEBUFFER (cogl_offscreen_new_with_texture (tex));
   state.offscreen_tex = tex;
 
   paint (&state);
diff --git a/tests/conform/test-color-mask.c b/tests/conform/test-color-mask.c
index e4ae4bd99..5df6527ae 100644
--- a/tests/conform/test-color-mask.c
+++ b/tests/conform/test-color-mask.c
@@ -87,7 +87,7 @@ test_color_mask (void)
 
 
       state.fbo[i] = COGL_FRAMEBUFFER (
-        cogl_offscreen_new_to_texture (state.tex[i]));
+        cogl_offscreen_new_with_texture (state.tex[i]));
 
       /* Clear the texture color bits */
       cogl_framebuffer_clear4f (state.fbo[i],
diff --git a/tests/conform/test-framebuffer-get-bits.c b/tests/conform/test-framebuffer-get-bits.c
index ac7ab5290..f1a85b281 100644
--- a/tests/conform/test-framebuffer-get-bits.c
+++ b/tests/conform/test-framebuffer-get-bits.c
@@ -10,14 +10,14 @@ test_framebuffer_get_bits (void)
                                    16, 16, /* width/height */
                                    COGL_PIXEL_FORMAT_A_8);
   CoglOffscreen *offscreen_a =
-    cogl_offscreen_new_to_texture (COGL_TEXTURE (tex_a));
+    cogl_offscreen_new_with_texture (COGL_TEXTURE (tex_a));
   CoglFramebuffer *fb_a = COGL_FRAMEBUFFER (offscreen_a);
   CoglTexture2D *tex_rgba =
     cogl_texture_2d_new_with_size (test_ctx,
                                    16, 16, /* width/height */
                                    COGL_PIXEL_FORMAT_RGBA_8888);
   CoglOffscreen *offscreen_rgba =
-    cogl_offscreen_new_to_texture (COGL_TEXTURE (tex_rgba));
+    cogl_offscreen_new_with_texture (COGL_TEXTURE (tex_rgba));
   CoglFramebuffer *fb_rgba = COGL_FRAMEBUFFER (offscreen_rgba);
 
   cogl_framebuffer_allocate (fb_a, NULL);
diff --git a/tests/conform/test-gles2-context.c b/tests/conform/test-gles2-context.c
index d5040e988..6b171c0f1 100644
--- a/tests/conform/test-gles2-context.c
+++ b/tests/conform/test-gles2-context.c
@@ -28,7 +28,7 @@ test_push_pop_single_context (void)
                                    cogl_framebuffer_get_width (test_fb),
                                    cogl_framebuffer_get_height (test_fb),
                                    COGL_PIXEL_FORMAT_ANY));
-  offscreen = cogl_offscreen_new_to_texture (offscreen_texture);
+  offscreen = cogl_offscreen_new_with_texture (offscreen_texture);
 
   pipeline = cogl_pipeline_new (test_ctx);
   cogl_pipeline_set_layer_texture (pipeline, 0, offscreen_texture);
@@ -152,7 +152,7 @@ create_gles2_context (CoglTexture **offscreen_texture,
                                    cogl_framebuffer_get_width (test_fb),
                                    cogl_framebuffer_get_height (test_fb),
                                    COGL_PIXEL_FORMAT_ANY));
-  *offscreen = cogl_offscreen_new_to_texture (*offscreen_texture);
+  *offscreen = cogl_offscreen_new_with_texture (*offscreen_texture);
 
   *pipeline = cogl_pipeline_new (test_ctx);
   cogl_pipeline_set_layer_texture (*pipeline, 0, *offscreen_texture);
diff --git a/tests/conform/test-offscreen.c b/tests/conform/test-offscreen.c
index e72ca607f..cd1ae4ab5 100644
--- a/tests/conform/test-offscreen.c
+++ b/tests/conform/test-offscreen.c
@@ -50,7 +50,7 @@ test_paint (TestState *state)
                                           COGL_PIXEL_FORMAT_RGBA_8888_PRE);
   tex = COGL_TEXTURE (tex_2d);
 
-  offscreen = cogl_offscreen_new_to_texture (tex);
+  offscreen = cogl_offscreen_new_with_texture (tex);
 
   /* Set a scale and translate transform on the window framebuffer
    * before switching to the offscreen framebuffer so we can verify it
@@ -131,7 +131,7 @@ test_flush (TestState *state)
                                               COGL_PIXEL_FORMAT_RGBA_8888_PRE);
       tex = COGL_TEXTURE (tex_2d);
 
-      offscreen = cogl_offscreen_new_to_texture (tex);
+      offscreen = cogl_offscreen_new_with_texture (tex);
 
       cogl_push_framebuffer (COGL_FRAMEBUFFER (offscreen));
 
diff --git a/tests/conform/test-readpixels.c b/tests/conform/test-readpixels.c
index f543fb09f..131b08b23 100644
--- a/tests/conform/test-readpixels.c
+++ b/tests/conform/test-readpixels.c
@@ -51,7 +51,7 @@ on_paint (ClutterActor *actor, void *state)
                                     FRAMEBUFFER_WIDTH * 4, /* rowstride */
                                     data);
   g_free (data);
-  offscreen = cogl_offscreen_new_to_texture (tex);
+  offscreen = cogl_offscreen_new_with_texture (tex);
 
   cogl_push_framebuffer (offscreen);
 
diff --git a/tests/conform/test-viewport.c b/tests/conform/test-viewport.c
index c437ec7c0..a1937c42a 100644
--- a/tests/conform/test-viewport.c
+++ b/tests/conform/test-viewport.c
@@ -217,7 +217,7 @@ on_paint (ClutterActor *actor, void *state)
                                     FRAMEBUFFER_WIDTH * 4, /* rowstride */
                                     data);
   g_free (data);
-  offscreen = cogl_offscreen_new_to_texture (tex);
+  offscreen = cogl_offscreen_new_with_texture (tex);
 
   cogl_push_framebuffer (offscreen);