Do you charge clients for a code audit before fixing their broken site?

Every time a new client asks us to patch an issue on an unfamiliar web app I struggle with whether to demand a paid diagnostic hour first or just take a wild guess at the pricing.

Clients hate paying twice but jumping straight into a fixed price quote without auditing the codebase is a fast track to working for free.

What pricing model works best for you when stepping into a codebase built by someone else?