The constant time property is considered the security standard for cryptographic code. Code following the constant time discipline is free from secret-dependent branches and memory accesses, and thus avoids leaking secrets through cache and timing side channels. Though security against side channel attacks is an important concern for secure cryptographic implementations, the constant time property makes a number of implicit assumptions that are fundamentally at odds with the reality of cryptographic code. We propose a notion of robust constant time parameterized by a notion of attacker model that better captures the realities of software security for cryptographic code.