Quaternary mixtures of water (A), and oil (B), a nonionic amphiphile (C), and an appropriately chosen fourth component offer an opportunity for searching for tricritical points (tcp) at atmospheric pressure. It is shown that for reaching a tcp, one has to couple an A-B-C mixture that shows the phase sequence 2 --> 3 --> 2BAR with rising temperature, with a second ternary mixture that shows a 2 --> 2BAR transition, the bar denoting in which of the two phases the amphiphile is mainly dissolved. With weakly structured solutions, that is, with short-chain amphiphiles as (C) this can be done by either adding an oil with a lower carbon number, or by adding a nonaqueous polar protic solvent such as formamide. With strongly structured solutions, that is, with long-chain amphiphiles, one has to add a short-chain amphiphile for destroying the structure as a prerequisite for reaching a tcp. Insofar, our earlier presumption that with long-chain amphiphiles, a tcp may also be reached, either by increasing their amphiphilicity or by lowering the carbon number of the oil, does not seem to apply. Experience shows that in A-B-C' mixtures with sufficiently short-chain amphiphiles as C' that separate into three phases: the amphiphile-rich middle phase always wets the A/B interface. If a short-chain amphiphile is added to an A-B-C mixture with a nonwetting middle phase one will, therefore, inevitably find a nonwetting --> wetting transition as one approaches a tcp.