  We characterize those planar Peano continua that are homotopy equivalent to
1-dimensional sets. While many planar Peano continua are not homotopically
1-dimensional, we prove that each has fundamental group that embeds in the
fundamental group of a 1-dimensional planar Peano continuum. We leave open the
following question: Is a planar Peano continuum homotopically 1- dimensional if
its fundamental group is isomorphic with the fundamental group of a
1-dimensional planar Peano continuum?
