diff --git a/cogl/cogl/cogl-private.h b/cogl/cogl/cogl-private.h
index 5a714fc1a..f842047f0 100644
--- a/cogl/cogl/cogl-private.h
+++ b/cogl/cogl/cogl-private.h
@@ -57,6 +57,7 @@ typedef enum
   COGL_PRIVATE_FEATURE_ALPHA_TEXTURES,
   COGL_PRIVATE_FEATURE_TEXTURE_SWIZZLE,
   COGL_PRIVATE_FEATURE_TEXTURE_MAX_LEVEL,
+  COGL_PRIVATE_FEATURE_TEXTURE_LOD_BIAS,
   COGL_PRIVATE_FEATURE_OES_EGL_SYNC,
   /* If this is set then the winsys is responsible for queueing dirty
    * events. Otherwise a dirty event will be queued when the onscreen
diff --git a/cogl/cogl/driver/gl/cogl-pipeline-opengl.c b/cogl/cogl/driver/gl/cogl-pipeline-opengl.c
index 8986e0466..d1e76f965 100644
--- a/cogl/cogl/driver/gl/cogl-pipeline-opengl.c
+++ b/cogl/cogl/driver/gl/cogl-pipeline-opengl.c
@@ -682,6 +682,22 @@ _cogl_sampler_gl_init (CoglContext *context, CoglSamplerCacheEntry *entry)
       GE (context, glSamplerParameteri (entry->sampler_object,
                                         GL_TEXTURE_WRAP_T,
                                         entry->wrap_mode_t) );
+
+      /* While COGL_PRIVATE_FEATURE_SAMPLER_OBJECTS implies support for
+       * GL_TEXTURE_LOD_BIAS in GL, the same is not true in GLES. So check,
+       * and also only apply GL_TEXTURE_LOD_BIAS in mipmap modes:
+       */
+      if (_cogl_has_private_feature (context,
+                                     COGL_PRIVATE_FEATURE_TEXTURE_LOD_BIAS) &&
+          entry->min_filter != GL_NEAREST &&
+          entry->min_filter != GL_LINEAR)
+        {
+          GLfloat bias = _cogl_texture_min_filter_get_lod_bias (entry->min_filter);
+
+          GE (context, glSamplerParameterf (entry->sampler_object,
+                                            GL_TEXTURE_LOD_BIAS,
+                                            bias));
+        }
     }
   else
     {
diff --git a/cogl/cogl/driver/gl/cogl-texture-2d-gl.c b/cogl/cogl/driver/gl/cogl-texture-2d-gl.c
index 23111eabf..61ccd75cf 100644
--- a/cogl/cogl/driver/gl/cogl-texture-2d-gl.c
+++ b/cogl/cogl/driver/gl/cogl-texture-2d-gl.c
@@ -470,6 +470,15 @@ _cogl_texture_2d_gl_flush_legacy_texobj_filters (CoglTexture *tex,
                                    tex_2d->gl_texture);
   GE( ctx, glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, mag_filter) );
   GE( ctx, glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, min_filter) );
+
+  if (_cogl_has_private_feature (ctx, COGL_PRIVATE_FEATURE_TEXTURE_LOD_BIAS) &&
+      min_filter != GL_NEAREST &&
+      min_filter != GL_LINEAR)
+    {
+      GLfloat bias = _cogl_texture_min_filter_get_lod_bias (min_filter);
+
+      GE (ctx, glTexParameterf (GL_TEXTURE_2D, GL_TEXTURE_LOD_BIAS, bias));
+    }
 }
 
 void
diff --git a/cogl/cogl/driver/gl/cogl-texture-gl-private.h b/cogl/cogl/driver/gl/cogl-texture-gl-private.h
index a8fbd2866..7804f8e7e 100644
--- a/cogl/cogl/driver/gl/cogl-texture-gl-private.h
+++ b/cogl/cogl/driver/gl/cogl-texture-gl-private.h
@@ -62,4 +62,11 @@ _cogl_texture_gl_generate_mipmaps (CoglTexture *texture);
 GLenum
 _cogl_texture_gl_get_format (CoglTexture *texture);
 
+static inline GLfloat
+_cogl_texture_min_filter_get_lod_bias (GLenum min_filter)
+{
+  return (min_filter == GL_NEAREST_MIPMAP_NEAREST ||
+          min_filter == GL_LINEAR_MIPMAP_NEAREST) ? -0.5f : 0.0f;
+}
+
 #endif /* _COGL_TEXTURE_GL_PRIVATE_H_ */
diff --git a/cogl/cogl/driver/gl/cogl-util-gl-private.h b/cogl/cogl/driver/gl/cogl-util-gl-private.h
index be8fa1eeb..2929e1c2d 100644
--- a/cogl/cogl/driver/gl/cogl-util-gl-private.h
+++ b/cogl/cogl/driver/gl/cogl-util-gl-private.h
@@ -250,4 +250,8 @@ cogl_gl_get_gpu_time_ns (CoglContext *context);
 #define GL_QUERY_RESULT 0x8866
 #endif
 
+#ifndef GL_TEXTURE_LOD_BIAS
+#define GL_TEXTURE_LOD_BIAS 0x8501
+#endif
+
 #endif /* _COGL_UTIL_GL_PRIVATE_H_ */
diff --git a/cogl/cogl/driver/gl/gl/cogl-driver-gl.c b/cogl/cogl/driver/gl/gl/cogl-driver-gl.c
index e498263aa..7c9449f5b 100644
--- a/cogl/cogl/driver/gl/gl/cogl-driver-gl.c
+++ b/cogl/cogl/driver/gl/gl/cogl-driver-gl.c
@@ -526,6 +526,13 @@ _cogl_driver_update_features (CoglContext *ctx,
   COGL_FLAGS_SET (private_features,
                   COGL_PRIVATE_FEATURE_TEXTURE_MAX_LEVEL, TRUE);
 
+  if (COGL_CHECK_GL_VERSION (gl_major, gl_minor, 3, 1) ||
+      _cogl_check_extension ("GL_EXT_texture_lod_bias", gl_extensions))
+    {
+      COGL_FLAGS_SET (private_features,
+                      COGL_PRIVATE_FEATURE_TEXTURE_LOD_BIAS, TRUE);
+    }
+
   if (ctx->glFenceSync)
     COGL_FLAGS_SET (ctx->features, COGL_FEATURE_ID_FENCE, TRUE);
 
diff --git a/cogl/cogl/driver/gl/gles/cogl-driver-gles.c b/cogl/cogl/driver/gl/gles/cogl-driver-gles.c
index de080a99d..0904f5a04 100644
--- a/cogl/cogl/driver/gl/gles/cogl-driver-gles.c
+++ b/cogl/cogl/driver/gl/gles/cogl-driver-gles.c
@@ -437,6 +437,12 @@ _cogl_driver_update_features (CoglContext *context,
                     COGL_FEATURE_ID_TEXTURE_RG,
                     TRUE);
 
+  if (_cogl_check_extension ("GL_EXT_texture_lod_bias", gl_extensions))
+    {
+      COGL_FLAGS_SET (private_features,
+                      COGL_PRIVATE_FEATURE_TEXTURE_LOD_BIAS, TRUE);
+    }
+
   if (context->glGenQueries && context->glQueryCounter && context->glGetInteger64v)
     COGL_FLAGS_SET (context->features, COGL_FEATURE_ID_TIMESTAMP_QUERY, TRUE);
 
diff --git a/cogl/cogl/gl-prototypes/cogl-all-functions.h b/cogl/cogl/gl-prototypes/cogl-all-functions.h
index fe9feaa5c..f98ea02f6 100644
--- a/cogl/cogl/gl-prototypes/cogl-all-functions.h
+++ b/cogl/cogl/gl-prototypes/cogl-all-functions.h
@@ -178,6 +178,10 @@ COGL_EXT_FUNCTION (void, glSamplerParameteri,
                    (GLuint sampler,
                     GLenum pname,
                     GLint param))
+COGL_EXT_FUNCTION (void, glSamplerParameterf,
+                   (GLuint sampler,
+                    GLenum pname,
+                    GLfloat param))
 COGL_EXT_END ()
 
 COGL_EXT_BEGIN (only_gl3, 3, 0,
diff --git a/cogl/cogl/gl-prototypes/cogl-core-functions.h b/cogl/cogl/gl-prototypes/cogl-core-functions.h
index e04b443ae..e362e797d 100644
--- a/cogl/cogl/gl-prototypes/cogl-core-functions.h
+++ b/cogl/cogl/gl-prototypes/cogl-core-functions.h
@@ -174,6 +174,8 @@ COGL_EXT_FUNCTION (void, glTexImage2D,
                     const GLvoid* pixels))
 COGL_EXT_FUNCTION (void, glTexParameteri,
                    (GLenum target, GLenum pname, GLint param))
+COGL_EXT_FUNCTION (void, glTexParameterf,
+                   (GLenum target, GLenum pname, GLfloat param))
 COGL_EXT_FUNCTION (void, glTexParameteriv,
                    (GLenum target, GLenum pname, const GLint* params))
 COGL_EXT_FUNCTION (void, glTexSubImage2D,