Along with minimizing parameter uncertainty, understanding the cause of temporal and spatial variability of the nucleated ice crystal number, Ni, is key to improving the representation of cirrus clouds in climate models. To this end, sensitivities of Ni to input variables like aerosol number and diameter provide valuable information about nucleation regime and efficiency for a given model formulation. Here we use the adjoint model of the adjoint of a cirrus formation parameterization (Barahona and Nenes, 2009b) to understand Ni variability for various ice-nucleating particle (INP) spectra. Inputs are generated with the Community Atmosphere Model version 5, and simulations are done with a theoretically derived spectrum, an empirical lab-based spectrum and two field-based empirical spectra that differ in the nucleation threshold for black carbon particles and in the active site density for dust. The magnitude and sign of Ni sensitivity to insoluble aerosol number can be directly linked to nucleation regime and efficiency of various INP. The lab-based spectrum calculates much higher INP efficiencies than field-based ones, which reveals a disparity in aerosol surface properties. Ni sensitivity to temperature tends to be low, due to the compensating effects of temperature on INP spectrum parameters; this low temperature sensitivity regime has been experimentally reported before but never deconstructed as done here. © Author(s) 2016.