diff --git a/pynumdiff/tests/test_diff_methods.py b/pynumdiff/tests/test_diff_methods.py
index 4299555..9cd7f0e 100644
--- a/pynumdiff/tests/test_diff_methods.py
+++ b/pynumdiff/tests/test_diff_methods.py
@@ -137,7 +137,7 @@ def spline_irreg_step(*args, **kwargs): return splinediff(*args, **kwargs)
                         [(0, 0), (1, 1), (0, 0), (1, 1)],
                         [(1, 0), (2, 2), (1, 0), (2, 2)],
                         [(1, 0), (3, 3), (1, 0), (3, 3)]],
-    polydiff: [[(-14, -15), (-14, -14), (0, -1), (1, 1)],
+    polydiff: [[(-14, -15), (-13, -14), (0, -1), (1, 1)],
                [(-14, -14), (-13, -13), (0, -1), (1, 1)],
                [(-14, -14), (-13, -13), (0, -1), (1, 1)],
                [(-2, -2), (0, 0), (0, -1), (1, 1)],
@@ -179,11 +179,11 @@ def spline_irreg_step(*args, **kwargs): return splinediff(*args, **kwargs)
                           [(0, 0), (1, 0), (0, -1), (1, 0)],
                           [(1, 1), (2, 2), (1, 1), (2, 2)],
                           [(1, 1), (3, 3), (1, 1), (3, 3)]],
-    jerk_sliding: [[(-15, -15), (-16, -16), (0, -1), (1, 0)],
+    jerk_sliding: [[(-25, -25), (-16, -16), (0, -1), (1, 0)],
                    [(-14, -14), (-14, -14), (0, -1), (0, 0)],
                    [(-14, -14), (-14, -14), (0, -1), (0, 0)],
-                   [(-1, -1), (0, 0), (0, -1), (1, 0)],
-                   [(0, 0), (2, 2), (0, 0), (2, 2)],
+                   [(-1, -1), (0, 0), (0, -1), (0, 0)],
+                   [(1, 0), (2, 2), (1, 0), (2, 2)],
                    [(1, 1), (3, 3), (1, 1), (3, 3)]],
     constant_velocity: [[(-25, -25), (-25, -25), (0, -1), (1, 1)],
                         [(-4, -5), (-3, -3), (0, -1), (1, 1)],
diff --git a/pynumdiff/utils/utility.py b/pynumdiff/utils/utility.py
index 77daf64..f7c3034 100644
--- a/pynumdiff/utils/utility.py
+++ b/pynumdiff/utils/utility.py
@@ -181,26 +181,27 @@ def slide_function(func, x, dt, kernel, *args, stride=1, pass_weights=False, **k
     if len(kernel) % 2 == 0: raise ValueError("Kernel window size should be odd.")
     half_window_size = (len(kernel) - 1)//2 # int because len(kernel) is always odd
 
-    weights = np.zeros((int(np.ceil(len(x)/stride)), len(x))) # Could be more space efficient
-    x_hats = np.zeros(weights.shape)
-    dxdt_hats = np.zeros(weights.shape)
+    x_hat = np.zeros(x.shape)
+    dxdt_hat = np.zeros(x.shape)
+    weight_sum = np.zeros(x.shape)
 
     for i,midpoint in enumerate(range(0, len(x), stride)): # iterate window midpoints
         # find where to index data and kernel, taking care at edges
-        window = slice(max(0, midpoint - half_window_size),
-                        min(len(x), midpoint + half_window_size + 1)) # +1 because slicing is exclusive of end
-        kslice = slice(max(0, half_window_size - midpoint),
-                        min(len(kernel), len(kernel) - (midpoint + half_window_size + 1 - len(x))))
+        start = max(0, midpoint - half_window_size)
+        end = min(len(x), midpoint + half_window_size + 1) # +1 because slicing is exclusive of end
+        window = slice(start, end)
 
-        # weights need to be renormalized if running off an edge
-        weights[i, window] = kernel if kslice.stop - kslice.stop == len(kernel) else kernel[kslice]/np.sum(kernel[kslice])
-        if pass_weights: kwargs['weights'] = weights[i, window]
+        kstart = max(0, half_window_size - midpoint)
+        kend = kstart + (end - start)
+        kslice = slice(kstart, kend)
 
-        # run the function on the window and save results
-        x_hats[i,window], dxdt_hats[i,window] = func(x[window], dt, *args, **kwargs)
+        w = kernel if (end-start) == len(kernel) else kernel[kslice]/np.sum(kernel[kslice])
+        if pass_weights: kwargs['weights'] = w
 
-    weights /= weights.sum(axis=0, keepdims=True) # normalize the weights
-    x_hat = np.sum(weights*x_hats, axis=0)
-    dxdt_hat = np.sum(weights*dxdt_hats, axis=0)
+        # run the function on the window and add weighted results to cumulative answers
+        x_window_hat, dxdt_window_hat = func(x[window], dt, *args, **kwargs)
+        x_hat[window] += w * x_window_hat
+        dxdt_hat[window] += w * dxdt_window_hat
+        weight_sum[window] += w # save sum of weights for normalization at the end
 
-    return x_hat, dxdt_hat
+    return x_hat/weight_sum, dxdt_hat/weight_sum