  We determine the smallest stretch factor among pseudo-Anosov maps with an
orientable invariant foliation on the closed nonorientable surfaces of genus 4,
5, 6, 7, 8, 10, 12, 14, 16, 18 and 20. We also determine the smallest stretch
factor of an orientation-reversing pseudo-Anosov map with orientable invariant
foliations on the closed orientable surfaces of genus 1, 3, 5, 7, 9 and 11. As
a byproduct, we obtain that the stretch factor of a pseudo-Anosov map on a
nonorientable surface or an orientation-reversing pseudo-Anosov map on an
orientable surface does not have Galois conjugates on the unit circle. This
shows that the techniques that were used to disprove Penner's conjecture on
orientable surfaces are ineffective in the nonorientable cases.
