diff --git a/palette.py b/palette.py
index 0f32de3..64cdd1a 100644
--- a/palette.py
+++ b/palette.py
@@ -7,17 +7,40 @@ import palette_ntsc
 
 
 class Palette:
-    SRGB = None
-    RGB = {}
-    CAM16UCS = {}
-
-    # How many successive screen pixels are used to compute output pixel 
+    # How many successive screen pixels are used to compute output pixel
     # palette index.
     PALETTE_DEPTH = None
 
+    # These next three dictionaries are all indexed by a tuple of (n-bit pixel
+    # value, NTSC phase), where:
+    #   n == PALETTE_DEPTH
+    #   MSB of the pixel value represents the current pixel on/off state
+    #   LSB of the pixel value is the on/off state of the pixel n-1 positions
+    #     to the left of current
+    #   NTSC phase = 0 .. 3 (= x position % 4)
+    #
+    # The choice of LSB --> MSB increasing from left to right across the
+    # screen matches the ordering used by the mapping of double hi-res memory
+    # to screen pixels.
+    #
+    # Dictionary values are the colour of the corresponding pixel in various
+    # colour spaces.
+
+    # Values are pixel colour in sRGB colour space.  Palettes are defined in
+    # this colour space.
+    SRGB = None
+
+    # Values are pixel colour in (linear) RGB colour space.  Dithering is
+    # performed in this colour space.
+    RGB = {}
+
+    # Values are pixel colour in CAM16-UCS colour space.  This is used for
+    # computing perceptual differences between colour values when optimizing
+    # the image dithering.
+    CAM16UCS = {}
+
     def __init__(self):
         self.RGB = {}
-        # XXX RGB and CAM16UCS should be indexed by (pixels_nbit, phase)
         for k, v in self.SRGB.items():
             self.RGB[k] = (np.clip(image.srgb_to_linear_array(v / 255), 0.0,
                                    1.0) * 255).astype(np.uint8)
@@ -25,15 +48,30 @@ class Palette:
                 self.CAM16UCS[k] = colour.convert(
                     v / 255, "sRGB", "CAM16UCS").astype(np.float32)
 
-    def _pixel_phase_shifts(self, phase_0_rgb):
-        rgb_phases = {}
-        for pixels, rgb in phase_0_rgb.items():
-            rgb_phases[pixels, 0] = rgb
-            for phase in range(1, 4):
-                msb = pixels & (1 << (self.PALETTE_DEPTH - 1))
-                pixels <<= 1 | (msb >> (self.PALETTE_DEPTH - 1))
-                rgb_phases[pixels, phase] = rgb
-        return rgb_phases
+    @staticmethod
+    def _pixel_phase_shifts(phase_3_srgb):
+        """Constructs dictionary of 4-bit pixel sequences for each NTSC phase.
+        Assumes PALETTE_DEPTH == 3
+
+        Args:
+            phase_3_rgb: dict mapping 4-bit pixel sequence to sRGB values,
+                for NTSC phase 3.
+
+        Returns:
+            dict mapping (shifted 4-bit pixel sequence, phase 0..3) to sRGB
+            values
+        """
+        srgb_phases = {}
+        for pixels, srgb in phase_3_srgb.items():
+            srgb_phases[pixels, 3] = srgb
+            # Rotate to compute 4-bit pixel sequences that produce the same
+            # colour for NTSC phases 0..2
+            for phase in range(0, 3):
+                lsb = pixels & 1
+                pixels >>= 1
+                pixels |= lsb << 3
+                srgb_phases[pixels, phase] = srgb
+        return srgb_phases
 
     def bitmap_to_idx(self, pixels: np.array) -> int:
         """Converts a bitmap of pixels into integer representation.
@@ -51,7 +89,7 @@ class Palette:
             # order to screen representation (i.e. LSB is the left-most
             # screen pixel), so we need to flip the order
             np.flip(pixels, axis=0)
-        )[0]
+        )[0] >> (8 - pixels.shape[0])
 
 
 class ToHgrPalette(Palette):
@@ -59,7 +97,7 @@ class ToHgrPalette(Palette):
     PALETTE_DEPTH = 4
 
     # Default tohgr/bmp2dhr palette
-    SRGB = {
+    SRGB = Palette._pixel_phase_shifts({
         0: np.array((0, 0, 0)),  # Black
         8: np.array((148, 12, 125)),  # Magenta
         4: np.array((99, 77, 0)),  # Brown
@@ -76,7 +114,7 @@ class ToHgrPalette(Palette):
         11: np.array((158, 172, 255)),  # Light blue
         7: np.array((93, 248, 133)),  # Aqua
         15: np.array((255, 255, 255)),  # White
-    }
+    })
 
 
 class OpenEmulatorPalette(Palette):
@@ -84,7 +122,7 @@ class OpenEmulatorPalette(Palette):
     PALETTE_DEPTH = 4
 
     # OpenEmulator
-    SRGB = {
+    SRGB = Palette._pixel_phase_shifts({
         0: np.array((0, 0, 0)),  # Black
         8: np.array((203, 0, 121)),  # Magenta
         4: np.array((99, 103, 0)),  # Brown
@@ -101,14 +139,14 @@ class OpenEmulatorPalette(Palette):
         11: np.array((160, 156, 244)),  # Light blue
         7: np.array((25, 243, 136)),  # Aqua
         15: np.array((244, 247, 244)),  # White
-    }
+    })
 
 
 class VirtualIIPalette(Palette):
     """4-bit palette exactly matching Virtual II emulator output."""
     PALETTE_DEPTH = 4
 
-    SRGB = {
+    SRGB = Palette._pixel_phase_shifts({
         0: np.array((0, 0, 0)),  # Black
         8: np.array((231, 36, 66)),  # Magenta
         4: np.array((154, 104, 0)),  # Brown
@@ -125,7 +163,7 @@ class VirtualIIPalette(Palette):
         11: np.array((120, 187, 255)),  # Light blue
         7: np.array((83, 250, 208)),  # Aqua
         15: np.array((255, 255, 255)),  # White
-    }
+    })
 
 
 class NTSCPalette(Palette):