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Another common way to reduce nesting (and, in some cases, to eliminated nested if-else blocks) is to use guard clauses.
A guard clause prevents complete entry to a subroutine unless a condition is met. It is a special case of an if-else block, and (if you use them) an exception to the "single entry, single exit" rule imposed by structured programming.
A guard clause allows:
to be written as
You see guard clauses all the time if you spend any time inside of standard modules like CGI.pm.
One of my standard refactorings for deeply nested code written by unrepentant structured programming purists is to reduce nesting by "pulling up" the guard clauses.
Update: I checked Martin Fowler's book Refactoring, and sure enough, he has a refactoring called "Replace Nested Conditional with Guard Clauses." He cites Kent Beck's 1997 book Smalltalk Best Practice Patterns, though Beck was codifying what was already a standard practice in the Smalltalk community.