  Self-loop alternating automata (SLAA) with B\"uchi or co-B\"uchi acceptance
are popular intermediate formalisms in translations of LTL to deterministic or
nondeterministic automata. This paper considers SLAA with generic
transition-based Emerson-Lei acceptance and presents translations of LTL to
these automata and back. Importantly, the translation of LTL to SLAA with
generic acceptance produces considerably smaller automata than previous
translations of LTL to B\"uchi or co-B\"uchi SLAA. Our translation is already
implemented in the tool LTL3TELA, where it helps to produce small deterministic
or nondeterministic automata for given LTL formulae.
