Passive neutrophils from five different individuals are rapidly aspirated at constant suction pressure and at room temperature into a pipet with a diameter of 4 microns. The excess suction pressures (i.e., the pressures in excess of the small threshold pressure required to produce continuous flow into the pipet) are 5000, 10,000 and 20,000 dyn/cm2 (0.5, 1 and 2 kPa) and are comparable to those encountered in the microcirculation. The rate of entry into the pipet is modeled with a linearized version of a theory by Yeung and Evans for the newtonian flow of a neutrophil into a pipet or pore. From this theory and measurements of the cell size and its rate of entry into the pipet, we can calculate a value for the cytoplasmic viscosity. A linear (newtonian) fit of the theory to the experimental data gives a value for the viscosity of 1050 poise. A non-linear fit predicts a decrease in the "apparent viscosity" from about 1500 poise at zero excess pressure to 1000 poise at an excess aspiration pressure of 20,000 dyn/cm2. Our experiments and analysis also allow us to calculate a value for the transit time through short pores over a wide range of excess aspiration pressures and pore diameters. For example, for a pore diameter of 3 microns and an aspiration pressure of 1250 dyn/cm2, we predict a transit time of about 70 s. At 6 microns and 20,000 dyn/cm2, the predicted transit time is only about 0.04 s.