Fixed price or hourly for fixing bugs on a site someone else built?

A client asks me to fix a bug on a site that another developer built. Before I open the code I cannot know whether it is a one-line fix or a tangle of old plugins and custom code that takes a day.

A fixed price is simple for the client but risky for me if the code is a mess. Hourly is fair to me but clients worry about the bill growing. A short paid diagnosis first, then a fixed price for the fix, is the middle path I have seen, but not every client accepts paying twice.

How do you price work on code you have not seen yet? Do you use a diagnosis step, a cap on hours, or something else, and how do clients react to it?