Using Brownian hydrodynamic simulation techniques, we study single polymers in shear. We investigate the effects of hydrodynamic interactions, excluded volume, chain extensibility, chain length and semiflexibility. The well-known stretching behavior with increasing shear rate [Formula: see text] is only observed for low shear [Formula: see text] < [Formula: see text] , where [Formula: see text] is the shear rate at maximum polymer extension. For intermediate shear rates [Formula: see text] < [Formula: see text] < [Formula: see text] the radius of gyration decreases with increasing shear with minimum chain extension at [Formula: see text] . For even higher shear [Formula: see text] < [Formula: see text] the chain exhibits again shear stretching. This non-monotonic stretching behavior is obtained in the presence of excluded-volume and hydrodynamic interactions for sufficiently long and inextensible flexible polymers, while it is completely absent for Gaussian extensible chains. We establish the heuristic scaling laws [Formula: see text] approximately N (-1.4) and [Formula: see text] approximately N (0.7) as a function of chain length N , which implies that the regime of shear-induced chain compression widens with increasing chain length. These scaling laws also imply that the chain response at high shear rates is not a universal function of the Weissenberg number Wi = [Formula: see text] [Formula: see text] anymore, where [Formula: see text] is the equilibrium relaxation time. For semiflexible polymers a similar non-monotonic stretching response is obtained. By extrapolating the simulation results to lengths corresponding to experimentally studied DNA molecules, we find that the shear rate [Formula: see text] to reach the compression regime is experimentally realizable.