  We study the relationship between exotic R^4's and Stein surfaces as it
applies to smoothing theory on more general open 4-manifolds. In particular, we
construct the first known examples of large exotic R^4's that embed in Stein
surfaces. This relies on an extension of Casson's Embedding Theorem for
locating Casson handles in closed 4-manifolds. Under sufficiently nice
conditions, we show that using these R^4's as end-summands produces uncountably
many diffeomorphism types while maintaining independent control over the
genus-rank function and the Taylor invariant.
