For what it's worth (not much, I guess), way back in the course of my second year of Greek (I was reading mostly Homer at the time), I made up a mnemonic for myself to recognize inflected forms containing the verbal base (root) from ἵεημι/ἱέναι: If you subtract prefix(es), augment (making allowances for the rough breathing), mood-markers (ο/ε, ω/η, οι/ι), and personal (or participial or infinitive) endings, and what's left is -η- or -ε- (-ἡ- or -ἑ-), then you've got a compound of ἵημι. Prior to "inventing" that mnemonic I used to get stumped by aorist forms like ἐφεῖτο, ἀφέθησαν or ἀφῇ. Pretty soon I was recognizing those forms right away when I encountered them in new texts that I was reading.
οὔτοι ἀπ’ ἀρχῆς πάντα θεοὶ θνητοῖς ὑπέδειξαν,
ἀλλὰ χρόνῳ ζητέοντες ἐφευρίσκουσιν ἄμεινον. (Xenophanes, Fragment 16)
Carl W. Conrad
Department of Classics, Washington University (Retired)