  We experimentally study a semiconductor laser subject to two optical
feedbacks in a free space setup. We show that the time delay signature,
manifesting itself in the chaotic output intensity, can be better suppressed
than in a laser with single feedback. We demonstrate that the control of the
feedback phase is essential to suppress the time delay signature, in contrast
to the one-delay case, and that the feedback phase also impacts the chaotic
bandwidth. By optimizing the feedback phase the time delay signature can be
reduced by a factor of 2 while maintaining a large chaotic bandwidth.
