The propagation and self‐focusing of short, intense laser pulses in a tenuous plasma is studied both analytically and numerically. Specifically, pulses of length of the order of a few plasma wavelengths and of intensity, which is large enough for relativistic self‐focusing to occur, are considered. Such pulses are of interest in various laser plasma acceleration schemes. It is found that these pulses are likely to be strongly affected by Raman instabilities. Two different regimes of instability, corresponding to large and small scattering angles, are found to be important. Small‐angle scattering is perhaps the most severe since it couples strongly with relativistic self‐focusing, leading the pulses to acquire significant axial and transverse structure in a time of the order of the self‐focusing time. Thus it will be difficult to propagate smooth self‐focused pulses through tenuous plasmas for distances longer than the Rayleigh length, except for pulse duration of the order of the plasma period.