High-resolution angle-resolved photoemission measurements were performed on single crystals of Bi2Sr2Ca1Cu2O8+delta with different oxygen stoichiometries. The data establish that the gap anisotropy (ratio of the gap along T-M to the gap along T-X) can be reversibly changed from similar to 20:1 (optimal or underdoped) to similar to 2:1 (overdoped). Differences in sample doping explain the conflicting reports on gap anisotropy in the literature. Possible effects of this change in gap anisotropy on the symmetry of the order parameter are discussed. There remains some ambiguity as to the relation between the order parameter and doping.