We describe internal test-case reduction, the method of test-case reduction employed by Hypothesis, a widely-used property-based testing library for Python. The key idea of internal test-case reduction is that instead of applying test-case reduction externally to generated test cases, we apply it internally, to the sequence of random choices made during generation, so that a test case is reduced by continually re-generating smaller and simpler test cases that continue to trigger some property of interest (e.g. a bug in the system under test). This allows for fully generic test-case reduction without any user intervention and without the need to write a specific test-case reducer for a particular application domain. It also significantly mitigates the impact of the test-case validity problem, by ensuring that any reduced test case is one that could in principle have been generated. We describe the rationale behind this approach, explain its implementation in Hypothesis, and present an extensive evaluation comparing its effectiveness with that of several other test-case reducers, including C-Reduce and delta debugging, on applications including Python auto-formatting, C compilers, and the SymPy symbolic math library. Our hope is that these insights into the reduction mechanism employed by Hypothesis will be useful to researchers interested in randomized testing and test-case reduction, as the crux of the approach is fully generic and should be applicable to any random generator of test cases.