diff --git a/libgimp/tests/test-palette.c b/libgimp/tests/test-palette.c
index ac292b18e5..72523b08e8 100644
--- a/libgimp/tests/test-palette.c
+++ b/libgimp/tests/test-palette.c
@@ -5,6 +5,7 @@
 #define GIMP_TEST_COLOR_R_U8   72
 #define GIMP_TEST_COLOR_G_U8   56
 #define GIMP_TEST_COLOR_B_U8   56
+#define EPSILON                1e-6f
 
 static GimpValueArray *
 gimp_c_test_run (GimpProcedure        *procedure,
@@ -74,16 +75,24 @@ gimp_c_test_run (GimpProcedure        *procedure,
   format2     = babl_format ("RGBA float");
   format2_bpp = babl_format_get_bytes_per_pixel (format2);
   fcolormap   = (gfloat *) gimp_palette_get_colormap (palette, format2, &n_colormap_colors, &n_bytes);
-  GIMP_TEST_END(fcolormap != NULL && n_colormap_colors == n_colors  &&
+  GIMP_TEST_END(fcolormap != NULL && n_colormap_colors == n_colors &&
                 format2 != format                                  &&
                 format2_bpp > format_bpp                           &&
                 n_colormap_colors * format2_bpp == n_bytes)
 
   GIMP_TEST_START("Comparing fourth palette color's RGB components from colormap in float format")
   gegl_color_get_pixel (color, format2, rgba);
-  GIMP_TEST_END(fcolormap[4 * GIMP_TEST_COLOR_IDX] == rgba[0]                  &&
-                fcolormap[4 * GIMP_TEST_COLOR_IDX + 1] == rgba[1] &&
-                fcolormap[4 * GIMP_TEST_COLOR_IDX + 2]== rgba[2])
+  /* XXX: whether to a colormap or to a GeglColor, I was expecting the
+   * conversion from palette format to target format to be done through
+   * exact same babl code path, hence equality to be perfect (i.e. no
+   * epsilon needed for float comparison). This is true on my machine,
+   * not on CI. Is it again some SSE2 inconsistency where sometimes
+   * conversion goes to SSE2, sometimes not, for the same run and same
+   * babl fish? Something else? To be further investigated.
+   */
+  GIMP_TEST_END(fabsf (fcolormap[4 * GIMP_TEST_COLOR_IDX] - rgba[0]) < EPSILON     &&
+                fabsf (fcolormap[4 * GIMP_TEST_COLOR_IDX + 1] - rgba[1]) < EPSILON &&
+                fabsf (fcolormap[4 * GIMP_TEST_COLOR_IDX + 2] - rgba[2]) < EPSILON)
 
   g_free (fcolormap);
 
diff --git a/libgimp/tests/test-palette.py b/libgimp/tests/test-palette.py
index dfcce9dfb5..2a656a72d7 100644
--- a/libgimp/tests/test-palette.py
+++ b/libgimp/tests/test-palette.py
@@ -9,6 +9,7 @@ GIMP_TEST_COLOR_FORMAT = "R'G'B' u8"
 GIMP_TEST_COLOR_R_U8   = 72
 GIMP_TEST_COLOR_G_U8   = 56
 GIMP_TEST_COLOR_B_U8   = 56
+EPSILON                = 1e-6
 
 pal = Gimp.Palette.get_by_name(GIMP_TEST_PALETTE)
 gimp_assert('gimp_palette_get_by_name()', type(pal) == Gimp.Palette)
@@ -52,19 +53,19 @@ gimp_assert('gimp_palette_get_colormap() in "RGBA float"',
 
 
 start = f2_bpp * GIMP_TEST_COLOR_IDX
-colormap_r = struct.unpack('f', colormap[start:start + 4])
-colormap_g = struct.unpack('f', colormap[start + 4:start + 8])
-colormap_b = struct.unpack('f', colormap[start + 8:start + 12])
+colormap_r = struct.unpack('f', colormap[start:start + 4])[0]
+colormap_g = struct.unpack('f', colormap[start + 4:start + 8])[0]
+colormap_b = struct.unpack('f', colormap[start + 8:start + 12])[0]
 
 rgb_bytes = colors[GIMP_TEST_COLOR_IDX].get_bytes(f2)
 rgb = rgb_bytes.get_data()
-palette_r = struct.unpack('f', rgb[:4])
-palette_g = struct.unpack('f', rgb[4:8])
-palette_b = struct.unpack('f', rgb[8:12])
+palette_r = struct.unpack('f', rgb[:4])[0]
+palette_g = struct.unpack('f', rgb[4:8])[0]
+palette_b = struct.unpack('f', rgb[8:12])[0]
 gimp_assert("Comparing fourth palette color's RGB components from colormap in float format",
-            colormap_r == palette_r and
-            colormap_g == palette_g and
-            colormap_b == palette_b)
+            abs(colormap_r - palette_r) < EPSILON and
+            abs(colormap_g - palette_g) < EPSILON and
+            abs(colormap_b - palette_b) < EPSILON)
 
 # Run the same tests through PDB: