Although elliptic curve cryptosystems are attractive candidates for implementing cryptography in memory constrained environments, in this context, one has to care about side channel attacks, which allow to reveal secret parameters by observing side channel information. Okeya and Takagi presented a fast countermeasure against side channel attacks on elliptic curves and qualified it as "flexible", since the user has full control on the ratio between memory consumption and efficiency. In this paper, we present two weaknesses in their scheme. We repair one of the weaknesses with a better implementation of their countermeasure, and recommend an additional countermeasure for repairing the second. Finally, we describe the situations where the repaired scheme is indeed flexible, that is, when it shows greater efficiency without compromising security.