  Lebesgue space bounds $L^{p_1}({\mathbb R}^1) \times L^{p_2}(^1) \to
L^q({\mathbb R}^1)$ are established for certain maximal bilinear operators. The
proof combines a trilinear smoothing inequality with Calder\'on-Zygmund theory.
  A reference to overlapping work of other authors on one observation has been
added.
