In Gram-negative bacteria, several trans-envelope complexes (TECs) have been identified that span the periplasmic space in order to facilitate lipid transport between the inner- and outer-membranes. While partial or near-complete structures of some of these TECs have been solved by conventional experimental techniques, most remain incomplete. Here we describe how a combination of computational approaches, constrained by experimental data, can be used to build complete atomic models for four TECs implicated in lipid transport in Escherichia coli. We use the DeepMind protein structure prediction algorithm, AlphaFold2, and a variant of it designed to predict protein complexes, AF2Complex, to predict the oligomeric states of key components of TECs and their likely interfaces with other components. After obtaining initial models of the complete TECs by superimposing predicted structures of subcomplexes, we use the membrane orientation prediction algorithm OPM to predict the likely orientations of the inner- and outer-membrane components in each TEC. Since, in all cases, the predicted membrane orientations in these initial models are tilted relative to each other, we devise a novel molecular mechanics-based strategy that we call membrane morphing that adjusts each TEC model until the two membranes are properly aligned with each other and separated by a distance consistent with estimates of the periplasmic width in E. coli. The study highlights the potential power of combining computational methods, operating within limits set by both experimental data and by cell physiology, for producing useable atomic structures of very large protein complexes.