Recent work established that some restricted-use objects, such as max registers, counters and atomic snapshots, admit polylogarithmic step-/complexity wait-free implementations using only reads and writes: when only polynomially-many updates are allowed, reading the object (by performing a ReadMax, CounterRead or Scan operation, depending on the object's type) incurs O(log N) steps (where N is the number of processes), which was shown to be optimal. But what about the step-/complexity of update operations? With these implementations, updating the object's state (by performing a WriteMax, Counter Increment or Update operation, depending on the object's type) requires Ω(log N) steps. The question that we address in this work is the following: are there read-optimal implementations of these restricted-use objects for which the asymptotic step-/complexity of update operations is sub-logarithmic?