A reader of a set of data accessors that includes readers and writer detects that a particular lock of a first collection of non-global locks associated with a data object of a computing environment is held by another accessor. After checking a blocking indicator, the reader uses a second lock (which is not part of the first collection) to obtain read access to the data object and implements its reads without acquiring the particular lock. Prior to implementing a write on the data object, a writer acquires at least some locks of the first collection, and sets the blocking indicator to prevent readers from using the second lock to obtain read access to the data object.