diff --git a/dither.pyx b/dither.pyx
index 31277df..109611e 100644
--- a/dither.pyx
+++ b/dither.pyx
@@ -464,7 +464,7 @@ def k_means_with_fixed_centroids(
     cdef int i, iteration, centroid_idx, num_fixed_centroids, num_random_centroids, best_centroid_idx
     cdef float[::1] point, centroid, new_centroid, old_centroid
     cdef float[:, ::1] centroids
-    cdef float best_dist, centroid_movement
+    cdef float best_dist, centroid_movement, dist
 
     centroids = np.zeros((n_clusters, 3), dtype=np.float32)
     if fixed_centroids is not None:
@@ -473,9 +473,9 @@ def k_means_with_fixed_centroids(
     num_random_centroids = n_clusters - num_fixed_centroids
 
     # TODO: kmeans++ initialization
+    cdef int rand_idx = random.randint(0, data.shape[0])
     for i in range(num_random_centroids):
-        centroids[num_fixed_centroids + i, :] = data[
-            random.randint(0, data.shape[0]), :]
+        centroids[num_fixed_centroids + i, :] = data[rand_idx, :]
 
     cdef int[::1] centroid_weights = np.zeros(n_clusters, dtype=np.int32)
     for iteration in range(iterations):
@@ -484,7 +484,8 @@ def k_means_with_fixed_centroids(
         for point in data:
             best_dist = 1e9
             best_centroid_idx = 0
-            for centroid_idx, centroid in enumerate(centroids):
+            for centroid_idx in range(n_clusters):
+                centroid = centroids[centroid_idx, :]
                 dist = colour_distance(centroid, point)
                 if dist < best_dist:
                     best_dist = dist
@@ -492,12 +493,11 @@ def k_means_with_fixed_centroids(
             closest_points[best_centroid_idx].append(point)
 
         centroid_movement = 0
-
         for centroid_idx, points in closest_points.items():
             centroid_weights[centroid_idx] = len(points)
             if centroid_idx < num_fixed_centroids:
                 continue
-            new_centroid = np.mean(np.array(points), axis=0)
+            new_centroid = np.median(np.array(points), axis=0)
             old_centroid = centroids[centroid_idx]
             centroid_movement += colour_distance(old_centroid, new_centroid)
             centroids[centroid_idx, :] = new_centroid