diff --git a/app/actions/channels-commands.c b/app/actions/channels-commands.c
index d7ffc1636c..842634cd99 100644
--- a/app/actions/channels-commands.c
+++ b/app/actions/channels-commands.c
@@ -54,6 +54,9 @@
 #include "gimp-intl.h"
 
 
+#define RGBA_EPSILON 1e-6
+
+
 /*  local function prototypes  */
 
 static void   channels_new_callback             (GtkWidget     *dialog,
@@ -504,12 +507,12 @@ channels_edit_attributes_callback (GtkWidget     *dialog,
 {
   GimpItem *item = GIMP_ITEM (channel);
 
-  if (strcmp (channel_name, gimp_object_get_name (channel))        ||
-      gimp_rgba_distance (channel_color, &channel->color) > 0.0001 ||
-      channel_visible       != gimp_item_get_visible (item)        ||
-      channel_linked        != gimp_item_get_linked (item)         ||
-      channel_color_tag     != gimp_item_get_color_tag (item)      ||
-      channel_lock_content  != gimp_item_get_lock_content (item)   ||
+  if (strcmp (channel_name, gimp_object_get_name (channel))              ||
+      gimp_rgba_distance (channel_color, &channel->color) > RGBA_EPSILON ||
+      channel_visible       != gimp_item_get_visible (item)              ||
+      channel_linked        != gimp_item_get_linked (item)               ||
+      channel_color_tag     != gimp_item_get_color_tag (item)            ||
+      channel_lock_content  != gimp_item_get_lock_content (item)         ||
       channel_lock_position != gimp_item_get_lock_position (item))
     {
       gimp_image_undo_group_start (image,
@@ -519,7 +522,7 @@ channels_edit_attributes_callback (GtkWidget     *dialog,
       if (strcmp (channel_name, gimp_object_get_name (channel)))
         gimp_item_rename (GIMP_ITEM (channel), channel_name, NULL);
 
-      if (gimp_rgba_distance (channel_color, &channel->color) > 0.0001)
+      if (gimp_rgba_distance (channel_color, &channel->color) > RGBA_EPSILON)
         gimp_channel_set_color (channel, channel_color, TRUE);
 
       if (channel_visible != gimp_item_get_visible (item))
diff --git a/app/actions/quick-mask-commands.c b/app/actions/quick-mask-commands.c
index 7bf9a9adad..ef3ee25a1e 100644
--- a/app/actions/quick-mask-commands.c
+++ b/app/actions/quick-mask-commands.c
@@ -42,6 +42,9 @@
 #include "gimp-intl.h"
 
 
+#define RGBA_EPSILON 1e-6
+
+
 /*  local function prototypes  */
 
 static void   quick_mask_configure_callback (GtkWidget     *dialog,
@@ -167,7 +170,7 @@ quick_mask_configure_callback (GtkWidget     *dialog,
 
   gimp_image_get_quick_mask_color (image, &old_color);
 
-  if (gimp_rgba_distance (&old_color, channel_color) > 0.0001)
+  if (gimp_rgba_distance (&old_color, channel_color) > RGBA_EPSILON)
     {
       gimp_image_set_quick_mask_color (image, channel_color);
       gimp_image_flush (image);
diff --git a/app/core/gimpchannel.c b/app/core/gimpchannel.c
index a4af92e760..42db772027 100644
--- a/app/core/gimpchannel.c
+++ b/app/core/gimpchannel.c
@@ -60,6 +60,8 @@
 #include "gimp-intl.h"
 
 
+#define RGBA_EPSILON 1e-6
+
 enum
 {
   COLOR_CHANGED,
@@ -1698,7 +1700,7 @@ gimp_channel_set_color (GimpChannel   *channel,
   g_return_if_fail (GIMP_IS_CHANNEL (channel));
   g_return_if_fail (color != NULL);
 
-  if (gimp_rgba_distance (&channel->color, color) > 0.0001)
+  if (gimp_rgba_distance (&channel->color, color) > RGBA_EPSILON)
     {
       if (push_undo && gimp_item_is_attached (GIMP_ITEM (channel)))
         {
diff --git a/app/core/gimpcontext.c b/app/core/gimpcontext.c
index ff43700f65..37885835af 100644
--- a/app/core/gimpcontext.c
+++ b/app/core/gimpcontext.c
@@ -57,10 +57,11 @@
 #include "gimp-intl.h"
 
 
+#define RGBA_EPSILON 1e-10
+
 typedef void (* GimpContextCopyPropFunc) (GimpContext *src,
                                           GimpContext *dest);
 
-
 #define context_find_defined(context, prop)                              \
   while (!(((context)->defined_props) & (1 << (prop))) && (context)->parent) \
     (context) = (context)->parent
@@ -2319,7 +2320,7 @@ static void
 gimp_context_real_set_foreground (GimpContext   *context,
                                   const GimpRGB *color)
 {
-  if (gimp_rgba_distance (&context->foreground, color) < 0.0001)
+  if (gimp_rgba_distance (&context->foreground, color) < RGBA_EPSILON)
     return;
 
   context->foreground = *color;
@@ -2370,7 +2371,7 @@ static void
 gimp_context_real_set_background (GimpContext   *context,
                                   const GimpRGB *color)
 {
-  if (gimp_rgba_distance (&context->background, color) < 0.0001)
+  if (gimp_rgba_distance (&context->background, color) < RGBA_EPSILON)
     return;
 
   context->background = *color;
diff --git a/app/core/gimppalette.c b/app/core/gimppalette.c
index 335bda6f7c..f5b848ca41 100644
--- a/app/core/gimppalette.c
+++ b/app/core/gimppalette.c
@@ -37,7 +37,9 @@
 
 #include "gimp-intl.h"
 
-#define EPSILON 1e-10
+
+#define RGB_EPSILON 1e-6
+
 
 /*  local function prototypes  */
 
@@ -648,11 +650,11 @@ gimp_palette_find_entry (GimpPalette      *palette,
       for (list = palette->colors; list; list = g_list_next (list))
         {
           entry = (GimpPaletteEntry *) list->data;
-          if (gimp_rgb_distance (&entry->color, color) < EPSILON)
+          if (gimp_rgb_distance (&entry->color, color) < RGB_EPSILON)
             return entry;
         }
     }
-  else if (gimp_rgb_distance (&start_from->color, color) < EPSILON)
+  else if (gimp_rgb_distance (&start_from->color, color) < RGB_EPSILON)
     {
       return start_from;
     }
@@ -674,7 +676,7 @@ gimp_palette_find_entry (GimpPalette      *palette,
           if (next)
             {
               entry = (GimpPaletteEntry *) next->data;
-              if (gimp_rgb_distance (&entry->color, color) < EPSILON)
+              if (gimp_rgb_distance (&entry->color, color) < RGB_EPSILON)
                 return entry;
 
               next = next->next;
@@ -683,7 +685,7 @@ gimp_palette_find_entry (GimpPalette      *palette,
           if (prev)
             {
               entry = (GimpPaletteEntry *) prev->data;
-              if (gimp_rgb_distance (&entry->color, color) < EPSILON)
+              if (gimp_rgb_distance (&entry->color, color) < RGB_EPSILON)
                 return entry;
 
               prev = prev->prev;
diff --git a/app/core/gimppalettemru.c b/app/core/gimppalettemru.c
index 7d34e157b4..fb1157d3c0 100644
--- a/app/core/gimppalettemru.c
+++ b/app/core/gimppalettemru.c
@@ -34,6 +34,8 @@
 #include "gimp-intl.h"
 
 
+#define RGBA_EPSILON 1e-4
+
 enum
 {
   COLOR_HISTORY = 1
@@ -205,7 +207,7 @@ gimp_palette_mru_add (GimpPaletteMru *mru,
     {
       GimpPaletteEntry *entry = list->data;
 
-      if (gimp_rgba_distance (&entry->color, color) < 0.0001)
+      if (gimp_rgba_distance (&entry->color, color) < RGBA_EPSILON)
         {
           found = entry;
 
@@ -228,7 +230,7 @@ gimp_palette_mru_add (GimpPaletteMru *mru,
               GimpPaletteEntry *entry2 = list2->data;
 
               if (gimp_rgba_distance (&entry->color,
-                                      &entry2->color) < 0.0001)
+                                      &entry2->color) < RGBA_EPSILON)
                 {
                   found = entry2;
 
diff --git a/app/widgets/gimpcolorframe.c b/app/widgets/gimpcolorframe.c
index 04c513e1d9..eaddd54306 100644
--- a/app/widgets/gimpcolorframe.c
+++ b/app/widgets/gimpcolorframe.c
@@ -36,6 +36,8 @@
 #include "gimp-intl.h"
 
 
+#define RGBA_EPSILON 1e-6
+
 enum
 {
   PROP_0,
@@ -566,7 +568,7 @@ gimp_color_frame_set_color (GimpColorFrame *frame,
       frame->sample_format  == sample_format  &&
       frame->x              == x              &&
       frame->y              == y              &&
-      gimp_rgba_distance (&frame->color, color) < 0.0001)
+      gimp_rgba_distance (&frame->color, color) < RGBA_EPSILON)
     {
       frame->color = *color;
       return;
diff --git a/app/widgets/gimpcolormapeditor.c b/app/widgets/gimpcolormapeditor.c
index a4ace88345..834c18046b 100644
--- a/app/widgets/gimpcolormapeditor.c
+++ b/app/widgets/gimpcolormapeditor.c
@@ -48,8 +48,8 @@
 #include "gimp-intl.h"
 
 
-#define BORDER  6
-#define EPSILON 1e-10
+#define BORDER      6
+#define RGB_EPSILON 1e-6
 
 #define HAVE_COLORMAP(image) \
         (image != NULL && \
@@ -458,7 +458,7 @@ gimp_colormap_editor_get_index (GimpColormapEditor *editor,
 
       gimp_image_get_colormap_entry (image, index, &temp);
 
-      if (gimp_rgb_distance (&temp, search) > EPSILON)
+      if (gimp_rgb_distance (&temp, search) > RGB_EPSILON)
         {
           gint n_colors = gimp_image_get_colormap_size (image);
           gint i;
@@ -467,7 +467,7 @@ gimp_colormap_editor_get_index (GimpColormapEditor *editor,
             {
               gimp_image_get_colormap_entry (image, i, &temp);
 
-              if (gimp_rgb_distance (&temp, search) < EPSILON)
+              if (gimp_rgb_distance (&temp, search) < RGB_EPSILON)
                 {
                   index = i;
                   break;
diff --git a/app/widgets/gimpcolorpanel.c b/app/widgets/gimpcolorpanel.c
index 2cc6c27605..4bf15b20fd 100644
--- a/app/widgets/gimpcolorpanel.c
+++ b/app/widgets/gimpcolorpanel.c
@@ -36,6 +36,8 @@
 #include "gimpcolorpanel.h"
 
 
+#define RGBA_EPSILON 1e-6
+
 enum
 {
   RESPONSE,
@@ -255,7 +257,7 @@ gimp_color_panel_color_changed (GimpColorButton *button)
       gimp_color_dialog_get_color (GIMP_COLOR_DIALOG (panel->color_dialog),
                                    &dialog_color);
 
-      if (gimp_rgba_distance (&color, &dialog_color) > 0.00001 ||
+      if (gimp_rgba_distance (&color, &dialog_color) > RGBA_EPSILON ||
           color.a != dialog_color.a)
         {
           gimp_color_dialog_set_color (GIMP_COLOR_DIALOG (panel->color_dialog),
diff --git a/app/widgets/gimpviewrenderer.c b/app/widgets/gimpviewrenderer.c
index ee3fc059bf..d67ea05b25 100644
--- a/app/widgets/gimpviewrenderer.c
+++ b/app/widgets/gimpviewrenderer.c
@@ -53,6 +53,8 @@
 #include "gimp-priorities.h"
 
 
+#define RGB_EPSILON 1e-6
+
 enum
 {
   UPDATE,
@@ -502,7 +504,7 @@ gimp_view_renderer_set_border_color (GimpViewRenderer *renderer,
   g_return_if_fail (GIMP_IS_VIEW_RENDERER (renderer));
   g_return_if_fail (color != NULL);
 
-  if (gimp_rgb_distance (&renderer->border_color, color))
+  if (gimp_rgb_distance (&renderer->border_color, color) > RGB_EPSILON)
     {
       renderer->border_color = *color;
 
diff --git a/libgimpwidgets/gimpcolorarea.c b/libgimpwidgets/gimpcolorarea.c
index 062be74f0c..d0acf3dcfd 100644
--- a/libgimpwidgets/gimpcolorarea.c
+++ b/libgimpwidgets/gimpcolorarea.c
@@ -45,6 +45,7 @@
  **/
 
 
+#define RGBA_EPSILON        1e-6
 #define DRAG_PREVIEW_SIZE   32
 #define DRAG_ICON_OFFSET    -8
 
@@ -535,7 +536,7 @@ gimp_color_area_set_color (GimpColorArea *area,
 
   priv = GET_PRIVATE (area);
 
-  if (gimp_rgba_distance (&priv->color, color) < 0.000001)
+  if (gimp_rgba_distance (&priv->color, color) < RGBA_EPSILON)
     return;
 
   priv->color = *color;