Informal logicians recognise the frequent use of unstated assumptions; some (e.g. Fisher) also recognise entertained arguments and recommend a suppositional approach (such as Mackie's) to conditional statements. It is here argued that these two be put together to make argument diagrams more accurate and subtle. Philosophical benefits also accrue: insights into Jackson's apparent violations of modus tollens and contraposition and McGee's counterexamples to the validity of modus ponens.