  We construct homotopically non-trivial maps from S^m to S^n with arbitrarily
small 3-dilation for certain pairs (m,n). The simplest example is m=4, n=3.
Other examples include arbitrarily large values of m and n. We show that a
homotopy class in pi_7(S^4) can be represented by maps with arbitrarily small
4-dilation if and only if the class is torsion.
