diff --git a/qpytorch/distributions/multivariate_qexponential.py b/qpytorch/distributions/multivariate_qexponential.py
index 5cd1ab8..6a55153 100644
--- a/qpytorch/distributions/multivariate_qexponential.py
+++ b/qpytorch/distributions/multivariate_qexponential.py
@@ -241,7 +241,12 @@ def log_prob(self, value: Tensor) -> Tensor:
         See :py:meth:`torch.distributions.Distribution.log_prob
         <torch.distributions.distribution.Distribution.log_prob>`.
         """
-        if settings.fast_computations.log_prob.off():
+        # The torch.distributions.MultivariateNormal fallback is Gaussian-only.
+        # Only use it when power == 2. When fast_computations.log_prob is off
+        # (e.g. BoTorch disables it on import; QePyTorch shares gpytorch.settings),
+        # falling back for power != 2 silently ignores `power` and returns the
+        # Gaussian log-density.
+        if settings.fast_computations.log_prob.off() and bool(torch.as_tensor(self.power == 2).all()):
             return super().log_prob(value)
 
         if self._validate_args: