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Here are some tips for conducting numpy fancy indexing quickly:

1. Use boolean indexing instead of integer indexing when possible. Boolean indexing can be faster than integer indexing because it avoids the need to sort the indices.

2. Use nested lists for multidimensional fancy indexing. This can be more efficient than using the flatten function to create a 1D array of indices.

3. Pre-allocate the output array to avoid unnecessary memory allocation during indexing operations.

4. Avoid creating copies of the array when possible. Use views or references to the original array instead.

5. Use numpy's built-in functions for common indexing operations, such as numpy.take, numpy.compress or numpy.choose. These functions are optimized for performance and can be faster than raw indexing operations.