Are Electron Scattering Data Consistent with a Small Proton Radius?

We determine the charge radius of the proton by analyzing the published low momentum transfer electron-proton scattering data from Mainz. We note that polynomial expansions of the form factor converge for momentum transfers squared below $4m_\pi^2$, where $m_\pi$ is the pion mass. Expansions with enough terms to fit the data but few enough not to overfit yield proton radii smaller than the CODATA or Mainz values and in accord with the muonic atom results. We also comment on analyses using a wider range of data, and overall obtain a proton radius $R_E=0.840(16)$ fm.