While measuring action spectra for phase-shifting the circadian clock of Chlamydomonas, we observed that light pulses started near the phase response curve (PRC) "breakpoint" caused a reduction of the amplitude of the phototactic rhythm and two unexpected effects: (1) nonmonotonic fluence response curves (FRCs), and (2) shortening of the period of the subsequent free-running rhythm. The reduction of the rhythm's amplitude is dependent upon both the fluence and wavelength of the light pulse. The results are consistent with the amplitude being dependent upon the perceived "strength" of the stimulus, and with the nonmonotonic FRCs and reduced amplitude reflecting a light-induced change of the pacemaker's state variables to a region of the phase plane close to the "singularity." The period change that is evoked by single stimuli exhibits novel characteristics: large changes in period and a phase specificity that correlates with "singular" behavior. These period changes also appear to be a function of the stimulus strength, but indirectly; the magnitude of the period change is most strongly correlated with the magnitude of the light-induced phase shift. These results are interpreted in the context of limit cycle models of circadian clocks, and are used to suggest new tactics for measuring action spectra of light-induced clock resetting.