diff --git a/fsl/fslview/gl/gl14/gltensor_frag.prog b/fsl/fslview/gl/gl14/gltensor_frag.prog
index c97343333f95cb95f73787d3cb1278e73754c0d5..72c5604176e87f2d60c08fa1579eaa3f360411c5 100644
--- a/fsl/fslview/gl/gl14/gltensor_frag.prog
+++ b/fsl/fslview/gl/gl14/gltensor_frag.prog
@@ -54,13 +54,15 @@ TEX voxValue, normVoxCoord, texture[0], 3D;
 ADD voxValue, voxValue, { 0.0, 0.0, 0.0, 1.0 };
 
 # Look up the modulation value
-# from the modulation texture
+# from the modulation texture -
+# initialise modValue transparency
+# to 1.0, so it doesn't corrupt
+# our voxel colour value later on
+MOV modValue, { 0.0, 0.0, 0.0, 1.0 };  
 TEX modValue, normVoxCoord, texture[1], 3D;
-ADD modValue, modValue, { 0.0, 0.0, 0.0, 1.0 };  
   
-# Use those values to look up
-# the colours for each xyz
-# direction
+# Use those values to look up the
+# colours for each xyz direction
 TEX xColour, voxValue.x, texture[2], 1D;
 TEX yColour, voxValue.y, texture[3], 1D;
 TEX zColour, voxValue.z, texture[4], 1D;
@@ -71,7 +73,7 @@ MOV voxColour,            xColour;
 ADD voxColour, voxColour, yColour;
 ADD voxColour, voxColour, zColour;
 
-# But take the average of the alpha channel
+# Take the average of the alpha channel
 MUL voxColour, voxColour, { 1.0, 1.0, 1.0, 0.333333 };
 
 # Apply the modulation factor
diff --git a/fsl/fslview/gl/gl14/gltensor_line_funcs.py b/fsl/fslview/gl/gl14/gltensor_line_funcs.py
index 37ea8033e12edf9ae9ecc1f14f35fdc8da2fde3f..54569aa3562aa2dab0f28aff3ef942e5f515d4b2 100644
--- a/fsl/fslview/gl/gl14/gltensor_line_funcs.py
+++ b/fsl/fslview/gl/gl14/gltensor_line_funcs.py
@@ -121,6 +121,7 @@ def draw(self, zpos, xform=None):
     # Transform the world coordinates to
     # floating point voxel coordinates
     dToVMat = display.displayToVoxMat
+    vToDMat = display.voxToDisplayMat
     
     voxCoords  = transform.transform(worldCoords, dToVMat).transpose()
     imageData  = image.data
@@ -157,23 +158,17 @@ def draw(self, zpos, xform=None):
     # make a bunch of vertices which represent lines 
     # (two vertices per line), centered at the origin
     # and scaled appropriately
-    vecs[:, xax] *= 0.5 * self.xpixdim
-    vecs[:, yax] *= 0.5 * self.ypixdim
+    vecs *= 0.5
+    vecs  = np.hstack((-vecs, vecs)).reshape((2 * nVoxels, 3))
 
-    # Flatten on the depth axis
-    vecs[:, zax]  = 0.0
-    vecs = np.hstack((-vecs, vecs)).reshape((2 * nVoxels, 3))
-
-    #
-    # TODO The above code assumes a correspondence
-    # between the image array axes and the display
-    # coordinate system axes. I'm not currently
-    # sure how to get around this.
-    #
+    # Offset each of those vertices by
+    # their original voxel coordinates
+    vecs += voxCoords.T.repeat(2, 0)
 
     # Translate the world coordinates
     # by those line vertices
-    worldCoords = worldCoords.repeat(2, 0) + vecs
+    worldCoords = transform.transform(vecs, vToDMat)
+    worldCoords[:, zax] = zpos
     worldCoords = np.array(worldCoords, dtype=np.float32).ravel('C')
 
     # Draw all the lines!
diff --git a/fsl/utils/transform.py b/fsl/utils/transform.py
index f8d427ca3bc09276442ded2312020db754b64969..b77526f25ae9a5704fdf7c59996d9d15b6323ed8 100644
--- a/fsl/utils/transform.py
+++ b/fsl/utils/transform.py
@@ -44,8 +44,8 @@ def scaleOffsetXform(scales, offsets):
     xform[2, 2] = scales[2]
 
     xform[3, 0] = offsets[0]
-    xform[3, 1] = offsets[0]
-    xform[3, 2] = offsets[0]
+    xform[3, 1] = offsets[1]
+    xform[3, 2] = offsets[2]
 
     return xform