This paper explores the possibility of controlling molecular weight distributions (MWDs) produced by linear free radical polymerization (FRP). We theoretically study pulsed laser free radical polymerization in the presence of a preprepared inert polymer matrix whose chains are longer than the entanglement threshold N-e. Under such conditions living chain termination is dominated by entanglements, and earlier theory for continuously initiated steady-state FRP predicts most termination events involve one long (entangled) and one short (unentangled) chain. When initiation is pulsed, we find three time scales are critical in determining the dead molecular weight distribution: T, the time between pulses; tau(short), the time for a living chain to grow from birth to length N-e; and tau(living) the mean living chain lifetime. If the condition tau(short) much less than T much less than tau(living) is satisfied, we find the dead MWD is multimodal and entirely different than the broad steady-state MWD. The MWD peaks have width approximate toN(e) and decay as similar to1/(N - N-i)(3/2) far from the peak centered at Ni. The envelope of the peaks is essentially the steady-state MWD. We show that even when the background polymer matrix follows a broad MWD, pulsing still produces a multimodal product provided the mean background chain length exceeds N-e and certain other conditions are satisfied. Hence, an alternative procedure is to generate the background by standard steady-state FRP carried to high conversion. Physically, the effects derive from short-long domination. Each pulse injects fresh short living chains with which already-present long living chains terminate readily, producing dead chains. But a time tau(short) later these new macroradicals have grown long and entangled, so termination and dead chain production are then effectively switched off until the next pulse arrives.