We study the measure independent character of Godel speed-up theorems. In particular, we strengthen Arbib's necessary condition for the occurrence of a Godel speed-up [2, p. 13] to an equivalence result and generalize Di Paola's speed-up theorem [4]. We also characterize undecidable theories as precisely those theories which possess consistent measure independent Godel speed-ups and show that a theory $\tau_2$ is a measure independent Godel speed-up of a theory $\tau_1$ if and only if the set of undecidable sentences of $\tau_1$ which are provable in $\tau_2$ is not recursively enumerable.