The compressive response of thick, quasi-isotropic, AS4/3501-6 laminates with geometric anomalies was investigated theoretically and experimentally. The specimens considered were rectilinear with nominal dimensions of 254 mm (10 in.) long, by 102 mm (4 in.) wide, by 29.9 mm (0.78 in.) thick. The anomalies were designed to simulate expected fit-up clearance conditions resulting from normal manufacturing tolerances in the sphere joint regions of the DARPA Man-Rated Demonstration Article. Tests were conducted both with unfilled fit-up gaps and with fit-up gaps filled with a polymer shimming material (Hysol EQ9394). Strains were monitored in the specimen gage sections and in regions of high strain concentration resulting from the manufacturing anomalies. Measured strains correlated well with predicted strains from an ABAQUS finite element analysis. For all test cases the specimens were able to withstand strains due to the anomalies when gage section strain reached 7000 με. One specimen with no anomalies was tested to failure in uniaxial compression and failed in the gage section at 614 MPa (89.0 ksi) and 13 500 με, which is equivalent to autoclave-cured, thin-section composite failure strains for this material system and layup.