We propose a variant of elliptic multiple polylogarithms that have at most
logarithmic singularities in all variables and satisfy a differential equation
without homogeneous term. We investigate several non-trivial elliptic two-loop
Feynman integrals with up to three external legs and express them in terms of
our functions. We observe that in all cases they evaluate to pure combinations
of elliptic multiple polylogarithms of uniform weight. This is the first time
that a notion of uniform weight is observed in the context of Feynman integrals
that evaluate to elliptic polylogarithms.Comment: 47 page