Most multiphoton imaging of biological specimens is performed using microscope objectives optimized for high image quality under wide-field illumination. We present a class of objectives designed de novo without regard for these traditional constraints, driven exclusively by the needs of fast multiphoton imaging in turbid media: the delivery of femtosecond pulses without dispersion and the efficient collection of fluorescence. We model the performance of one such design optimized for a typical brain-imaging setup and show that it can greatly outperform objectives commonly used for this task.