  We identify three 3-graphs on five vertices each missing in all known
extremal configurations for Turan's (3,4)-problem and prove Turan's conjecture
for 3-graphs that are additionally known not to contain any induced copies of
these 3-graphs. Our argument is based on an (apparently) new technique of
"indirect interpretation" that allows us to retrieve additional structure from
hypothetical counterexamples to Turan's conjecture, but in rather loose and
limited sense. We also include two miscellaneous calculations in flag algebras
that prove similar results about some other additional forbidden subgraphs.
