diff --git a/sklearn/covariance/robust_covariance.py b/sklearn/covariance/robust_covariance.py
index afacb1fa4a690..1d80b34fc4ce1 100644
--- a/sklearn/covariance/robust_covariance.py
+++ b/sklearn/covariance/robust_covariance.py
@@ -118,7 +118,7 @@ def _c_step(X, n_support, random_state, remaining_iterations=30,
     # Iterative procedure for Minimum Covariance Determinant computation
     det = fast_logdet(covariance)
     previous_det = np.inf
-    while (det < previous_det) and (remaining_iterations > 0):
+    while (det < previous_det) and (remaining_iterations > 0) and not (np.isinf(det)):
         # save old estimates values
         previous_location = location
         previous_covariance = covariance
@@ -140,14 +140,9 @@ def _c_step(X, n_support, random_state, remaining_iterations=30,
 
     previous_dist = dist
     dist = (np.dot(X - location, precision) * (X - location)).sum(axis=1)
-    # Catch computation errors
+    # Check if best fit already found (det => 0, logdet => -inf)
     if np.isinf(det):
-        raise ValueError(
-            "Singular covariance matrix. "
-            "Please check that the covariance matrix corresponding "
-            "to the dataset is full rank and that MinCovDet is used with "
-            "Gaussian-distributed data (or at least data drawn from a "
-            "unimodal, symmetric distribution.")
+        results = location, covariance, det, support, dist
     # Check convergence
     if np.allclose(det, previous_det):
         # c_step procedure converged
@@ -361,9 +356,10 @@ def fast_mcd(X, support_fraction=None,
 
     X = np.asarray(X)
     if X.ndim == 1:
-        X = np.reshape(X, (1, -1))
-        warnings.warn("Only one sample available. "
-                      "You may want to reshape your data array")
+        X = np.reshape(X, (-1, 1))
+        warnings.warn("1D array passed in. "
+                      "Assuming the array contains samples, not features. "
+                      "You may wish to reshape your data.")
     n_samples, n_features = X.shape
 
     # minimum breakdown value