A non-solipsist form of presentness is usually thought to require the non-relative co-presentness of space-like separated events, where this requirement further implies the non-relative simultaneity of these events. Since special relativity is thought to rule out any global, non-relative simultaneity, typical non-solipsist forms of presentness are taken to be inconsistent with special relativity. To address this problem, we re-explain the relationship between the non-solipsism of presentness and co-presentness by appealing to metaphysical indeterminacy. We propose presentness indeterminacy, the thesis that where (...) an event, p, is determinately present, any event in space-like relation to p lacks a determinate tense. We argue that for many theories of time, indeterminate co-presentness is all that the non-solipsism of presentness requires. Since there is no determinate co-presentness, the inconsistency between presentness and special relativity in these theories disappears. (shrink)