  With the aim of extracting the pion charge radius, we analyse extant precise
pion+electron elastic scattering data on $Q^2 \in [0.015,0.144]\,$GeV$^2$ using
a method based on interpolation via continued fractions augmented by
statistical sampling. The scheme avoids any assumptions on the form of function
used for the representation of data and subsequent extrapolation onto
$Q^2\simeq 0$. Combining results obtained from the two available data sets, we
obtain $r_\pi = 0.640(7)\,$fm, a value $2.4\,\sigma$ below today's commonly
quoted average. The tension may be relieved by collection and similar analysis
of new precise data that densely cover a domain which reaches well below $Q^2 =
0.015\,$GeV$^2$. Considering available kaon+electron elastic scattering data
sets, our analysis reveals that they contain insufficient information to
extract an objective result for the charged-kaon radius, $r_K$. New data with
much improved precision, low-$Q^2$ reach and coverage are necessary before a
sound result for $r_K$ can be recorded.
