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We describe recent progress on the JILA Sr optical frequency standard, which has a systematic uncertainty at the 10-16 fractional frequency level. The dominant contributions to the systematic error are from blackbody radiation shifts and collisional shifts. We discuss the blackbody radiation shift and propose measurements and experimental protocols that should reduce its systematic contribution. We discuss how collisional frequency shifts can arise in an optical lattice clock employing fermionic atoms, and experimentally demonstrate how the uncertainty in this density-dependent correction to the clock frequency is reduced.