  Noether's first theorem does not establish a one-way explanatory arrow from
symmetries to conservation laws, but such an arrow is widely assumed in
discussions of the theorem in the physics and philosophy literature. It is
argued here that there are pragmatic reasons for privileging symmetries, even
if they do not strictly justify explanatory priority. To this end, some
practical factors are adduced as to why Noether's direct theorem seems to be
more well-known and exploited than its converse, with special attention being
given to the sometimes overlooked nature of Noether's converse result and to
its strengthened version due to Luis Mart\'inez Alonso in 1979 and Peter Olver
in 1986.
