Finding optimal word lengths in digital signal processing systems has been one of the primary mechanisms for reducing complexity. Recently, this topic has been explored in a broader approximate computing context, where architectures allowing for fine-grain control of hardware or software accuracy have been proposed. One of the obstacles for adoption of fine-grain scaling techniques is that they require determining the precision of all intermediate values at all possible operation points, making simulation-based optimization infeasible. In this chapter, we study efficient analytical heuristics to find optimal sets of word lengths for all variables and operations in a dataflow graph constrained by mean squared error type of metrics. We apply our method to several industrial-strength examples. Our results show a more than 5,000x improvement in optimization time compared to an efficient simulation-based word length optimization method with less than 10 % estimation error across a range of target quality metrics.