Preferences elicited with matching and choice usually diverge (as characterised by preference reversals), violating a basic rationality requirement, namely, procedure invariance. We report the results of an experiment that shows that preference reversals between matching (Standard Gamble in our case) and choice are reduced when the matching task is conducted using nontransparent methods. Our results suggest that techniques based on nontransparent methods are less influenced by biases (i.e., compatibility effects) than transparent methods. We also observe that imprecision of preferences influences the degree of preference reversals. The preference reversal phenomenon is less strong in subjects with more precise preferences.