diff --git a/curvlinops/inverse.py b/curvlinops/inverse.py
index 6473a8e..1ccacb4 100644
--- a/curvlinops/inverse.py
+++ b/curvlinops/inverse.py
@@ -430,14 +430,12 @@ def _compute_inv_damped_eigenvalues(
         else:
             inv_damped_eigenvalues = {}
             for p_name, pos in param_pos.items():
-                if p_name == "weight":
-                    inv_damped_eigenvalues[pos] = (
-                        outer(ggT_eigvals, aaT_eigvals).add_(self._damping).pow_(-1)
-                    )
-                else:
-                    inv_damped_eigenvalues[pos] = ggT_eigvals.add(self._damping).pow_(
-                        -1
-                    )
+                inv_damped_eigenvalues[pos] = (
+                    outer(ggT_eigvals, aaT_eigvals)
+                    if p_name == "weight"
+                    else ggT_eigvals
+                )
+                inv_damped_eigenvalues[pos].add_(self._damping).pow_(-1)
         return inv_damped_eigenvalues
 
     def _compute_inverse_factors(
@@ -536,8 +534,8 @@ def _compute_or_get_cached_inverse(
             return aaT_inv, ggT_inv, None
 
         if self._A._correct_eigenvalues:
-            aaT_inv = self._A._input_covariances_eigenvectors.get(name)
-            ggT_inv = self._A._gradient_covariances_eigenvectors.get(name)
+            aaT_eigenvecs = self._A._input_covariances_eigenvectors.get(name)
+            ggT_eigenvecs = self._A._gradient_covariances_eigenvectors.get(name)
             eigenvalues = self._A._corrected_eigenvalues.get(name)
             if isinstance(eigenvalues, dict):
                 inv_damped_eigenvalues = {}
@@ -545,16 +543,17 @@ def _compute_or_get_cached_inverse(
                     inv_damped_eigenvalues[key] = val.add(self._damping).pow_(-1)
             elif isinstance(eigenvalues, Tensor):
                 inv_damped_eigenvalues = eigenvalues.add(self._damping).pow_(-1)
-        else:
-            aaT = self._A._input_covariances.get(name)
-            ggT = self._A._gradient_covariances.get(name)
-            aaT_inv, ggT_inv, inv_damped_eigenvalues = self._compute_inverse_factors(
-                aaT, ggT, name
-            )
+            return aaT_eigenvecs, ggT_eigenvecs, inv_damped_eigenvalues
+
+        aaT = self._A._input_covariances.get(name)
+        ggT = self._A._gradient_covariances.get(name)
+        aaT_inv, ggT_inv, inv_damped_eigenvalues = self._compute_inverse_factors(
+            aaT, ggT, name
+        )
 
-            if self._cache:
-                self._inverse_input_covariances[name] = aaT_inv
-                self._inverse_gradient_covariances[name] = ggT_inv
+        if self._cache:
+            self._inverse_input_covariances[name] = aaT_inv
+            self._inverse_gradient_covariances[name] = ggT_inv
 
         return aaT_inv, ggT_inv, inv_damped_eigenvalues