  Cells employ control strategies to maintain a stable size. Dividing at a
target size (the `sizer' strategy) is thought to produce the tightest size
distribution. However, this result follows from phenomenological models that
ignore the molecular mechanisms required to implement the strategy. Here we
investigate a simple mechanistic model for exponentially growing cells whose
division is triggered at a molecular abundance threshold. We find that size
noise inherits the molecular noise and is consequently minimized not by the
sizer but by the `adder' strategy, where a cell divides after adding a target
amount to its birth size. We derive a lower bound on size noise that agrees
with publicly available data from six microfluidic studies on Escherichia coli
bacteria.
