Unidirectional basalt fiber rods consolidated with an aramid sleeve were measured for compression strength after impact at various energy levels and compared to undamaged control specimens. These structural elements represent local members of open three-dimensional composite lattice structures (e.g., based on isogrid or IsoTruss® technologies) that are continuously fabricated using advanced three-dimensional braiding techniques. The unidirectional core specimens, nominally 8 mm (5/16") and 11 mm (7/16") in diameter, were manufactured using bi-directional braided sleeves or unidirectional spiral sleeves with full or partial (approximately half) coverage of the core fibers. The 51 mm (2") specimens were shorter than the critical buckling length, ensuring the formation of kink bands, typical of strength-controlled compression failure of unidirectional composites. The test results indicate an approximate decrease in the average undamaged compression strength of approximately 1/3 and 2/3 when impacted with 5 J (3.7 ft-lbs) and 10 J (7.4 ft-lbs) for the 8 mm (5/16") diameter specimens and 10 J (7.4 ft-lbs.) and 20 J (14.8 ft-lbs.) for the 11 mm (7/16") diameter specimens, respectively. The aramid sleeves improved the damage tolerance of the composite members, with the amount of coverage having the greatest effect; full coverage exhibiting up to 45% greater strength than partial coverage. Braided sleeves improved compression strength after impact by up to 23% over spiral sleeves, but generally had little effect on damage tolerance. Larger diameter specimens tend to be more resistant to damage than those specimens of a smaller diameter. The compressive material properties for undamaged basalt composites are also presented with the average compressive strength being 800 MPa (116 ksi).