Efforts to establish the mechanisms of laser sputtering have been severely hampered because of a number of inconsistencies. These include time-of-flight (TOF) temperatures which were too high for normally emitted particles, were too low for obliquely emitted particles, and increased with the mass when several species were co-sputtered. At the same time the angular distributions were rarely of the expected form, cos θ, but rather spanned the interval cos 4θ to cos 10θ. We argue that the common feature in all cases is the known or suspected occurrence of near-surface gas-phase collisions, also termed Knudsen-layer formation. To this end we establish in the present work analytical solutions for the TOF signals for both a one and two-component system when there are sufficient collisions for a fully developed Knudsen layer, insufficient collisions for adiabatic expansion, and the detector is permitted to be off-axis. The properties of the solutions include (i) a shifting of the TOF spectrum to higher velocities for normal emission and (to a limited extent) to lower velocities for oblique emission, (ii) a temperature which appears to increase with the mass when several species are co-sputtered, as well as (iii) angular distributions similar to cos 4θ.