Uniform spheres of (Yb0.98RE0.02)PO4 orthophosphate (RE=Ho, Er, and Tm, respectively) were synthesized via a homogeneous precipitation procedure mediated by SO42- anions. The as-precipitated and 1100 degrees C calcined products were determined via laser-diffraction particle sizing to have the average diameters of 2.04 +/- 0.67 and 1.80 +/- 0.93m, respectively. The upconversion luminescence of RE3+ under sensitization by the host Yb3+ was studied for the calcination products under 978nm laser excitation, and it was found that the emissions are dominated by a red band at 650nm for Ho3+ (F-5(5) I-5(8) transition), similarly strong green (515-565nm, H-2(11/2)/S-4(3/2) I-4(15/2) transition) and red (640-680nm, F-4(9/2) I-4(15/2) transition) bands for Er3+, and a near-infrared band at 800nm for Tm3+ (H-3(4) H-3(6) transition). The number of laser photons needed to populate the emitting state was determined by varying the excitation power, and the possible photon reactions leading to the observed upconversion were discussed.