diff --git a/src/iterative_ensemble_smoother/experimental.py b/src/iterative_ensemble_smoother/experimental.py
index df8886c8..77b68595 100644
--- a/src/iterative_ensemble_smoother/experimental.py
+++ b/src/iterative_ensemble_smoother/experimental.py
@@ -11,11 +11,14 @@
 
 
 class RowScaling:
+    def __init__(self, alpha=1.0):
+        """Alpha is the strength of the update."""
+        assert 0 <= alpha <= 1.0
+        self.alpha = alpha
+
     def multiply(self, X, K):
-        """Takes a matrix X and a matrix K and performs X @ K."""
-        # TODO: Not sure why a RowScaling class is needed if
-        # all that it's used for is matrix multiplication
-        return X @ K
+        """Takes a matrix X and a matrix K and performs alpha * X @ K."""
+        return X @ (K * self.alpha)
 
 
 def ensemble_smoother_update_step_row_scaling(
@@ -96,8 +99,11 @@ def ensemble_smoother_update_step_row_scaling(
     covariance = np.exp(rng.normal(size=num_observations))
     observations = rng.normal(size=num_observations, loc=1)
 
+    # Split up X into groups of
     row_groups = [(0,), (1, 2), (4, 5, 6), tuple(range(7, 100))]
-    X_with_row_scaling = [(X[idx, :], RowScaling()) for idx in row_groups]
+    X_with_row_scaling = [
+        (X[idx, :], RowScaling(alpha=1 / (i + 1))) for i, idx in enumerate(row_groups)
+    ]
     X_before = deepcopy(X_with_row_scaling)
 
     X_with_row_scaling_updated = ensemble_smoother_update_step_row_scaling(