Lifetimes of excited states of the phosphorus isotopes 33,34,35,3615P have been measured using the differential recoil distance method. The isotopes of phosphorus were populated in binary grazing reactions initiated by a beam of 36S ions of energy 225 MeV incident on a thin 208Pb target which was mounted in the Cologne plunger apparatus. The combination of the PRISMA magnetic spectrometer and an early implementation of the AGATA γ-ray tracking array was used to detect γ rays in coincidence with projectile-like nuclear species. Lifetime measurements of populated states were measured within the range from about 1 to 100 ps. The number of states for which lifetime measurements were possible was limited by statistics. For 33P, lifetime limits were determined for the first 3/2+ and 5/2+ states at 1431 keV and 1848 keV, respectively; the results are compared with previous published lifetime values. The lifetime of the first 2+ state of 34P at 429 keV was determined and compared with earlier measurements. For 35P, the states for which lifetimes, or lifetime limits, were determined were those at 2386, 3860, 4101, and 4493 keV, with Jπ values of 3/2+, 5/2+, 7/21−, and 7/22−, respectively. There have been no previous published lifetimes for states in this nucleus. A lifetime was measured for the stretched π(1f7/2)⊗ν(1f7/2) Jπ = (7+) state of 36P at 5212 keV and a lifetime limit was established for the stretched π(1d3/2)⊗ν(1f7/2) Jπ= (5−) state at 2030 keV. There are no previously published lifetimes for states of 36P. Measured lifetime values were compared with the results of state-of-the-art shell-model calculations based on the PSDPF effective interaction. In addition, measured branching ratios, published mixing ratios, and electromagnetic transition rates, where available, have been compared with shell-model values. In general, there is good agreement between experiment and shell model; however there is evidence that the shell-model values of the M1 transition rates for the 3/21+ → 1/2+ (ground state) and 5/21+ → 3/21+ transitions in 33P underestimate the experimental values by a factor of between 5 and 10. In 35P there are some disagreements between experimental and shell-model values of branching ratios for the first and second excited 7/2− states. In particular, there is a serious disagreement for the decay characteristics of the second 7/2− state at 4493 keV, for which the shell-model counterpart lies at 4754 keV. In this case, the shell-model competing electromagnetic decay branches are dominated by E1 and M1 transitions.