Unidirectional carbon fiber and fiberglass epoxy composite elements consolidated with aramid sleeves were radially impacted at 5 J (3.7 ft-lbs) and 10 J (7.4 ft-lbs), tested under compression, 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). Advanced three-dimensional braiding techniques were used to continuously fabricate these specimens. The unidirectional core specimens, 8 mm (5/16 in) in diameter, were manufactured with various sleeve patterns. Bi-directional braided sleeves and unidirectional spiral sleeves ranged from a nominal full to half coverage. These specimens were tested for compression strength after impact. This research used an unsupported length of 50.8 mm (2.0 in) specimens to ensure a strength-controlled compression failure. Compression strength of undamaged unidirectional carbon fiber and fiberglass epoxy composites is virtually unaffected by sleeve type and sleeve coverage. Fiberglass/epoxy configurations exhibited approximately 1/2 and 2/3 reduction in compression strength relative to undamaged configurations after impact with 5 J (3.7 ft-lbs) and 10 J (7.4 ft-lbs), respectively. Increasing aramid sleeve coverage and/or increasing the interweaving of an aramid sleeve (i.e., braid vs. spiral) increases the damage tolerance of fiberglass/epoxy composite elements. Damaged carbon/epoxy composites exhibited an approximate decrease in strength of 70% and 75% after 5 J and 10 J of impact, respectively, relative to undamaged configurations. The results verify that an aramid sleeve, regardless of type (braid or spiral), facilitates consolidation of the carbon fiber and fiberglass epoxy core. Not surprisingly, full coverage configurations exhibit greater compression strength after impact than half coverage configurations.