Previous algorithms for feedback-directed unit test generation iteratively create sequences of API calls by executing partial tests and by adding new API calls at the end of the test. These algorithms are challenged by a popular class of APIs: higher-order functions that receive callback arguments, which often are invoked asynchronously. Existing test generators cannot effectively test such APIs because they only sequence API calls, but do not nest one call into the callback function of another. This paper presents Nessie, the first feedback-directed unit test generator that supports nesting of API calls and that tests asynchronous callbacks. Nesting API calls enables a test to use values produced by an API that are available only once a callback has been invoked, and is often necessary to ensure that methods are invoked in a specific order. The core contributions of our approach are a tree-based representation of unit tests with callbacks and a novel algorithm to iteratively generate such tests in a feedback-directed manner. We evaluate our approach on ten popular JavaScript libraries with both asynchronous and synchronous callbacks. The results show that, in a comparison with LambdaTester, a state of the art test generation technique that only considers sequencing of method calls, Nessie finds more behavioral differences and achieves slightly higher coverage. Notably, Nessie needs to generate significantly fewer tests to achieve and exceed the coverage achieved by the state of the art.