(This diagram that appeared in Cognitive Systems 1 sums up my work in this area)

Diagram - two stages of processing

Reviewing in the 1970s experimental literature on the right-sided speech advantage (widely known as "the right-ear advantage = REA")   two broad generalizations seemed well supported to me:
---(i) dichotic (different stimuli to the two ears at the same time) lateral differences arise at an early stage of speech processing, and
---(ii) ear differences are much easier to show with dichotic than monaural (one stimulus to one ear) presentation of the speech.

I believe both facts can be explained with minimal assumptions about underlying neural function, as follows.
(a) When listening to a syllable a "limited capacity channel" in our perceptual system assigns each distinct part of the incoming acoustic waveform to a particular phonetic category (e.g. /b/, /d/, /g/, /a/ etc).
(b) The internal trace of one of the dichotic stimuli must wait in temporary (“buffer”) storage while the other is being assigned its constituent phonemes.
(c) The information in this buffer is rapidly lost, which is what causes better report of the first stimulus processed.
(d) Following passage through the “phonetic categorisation” gate, traces are held in a much more durable form and do not decay at a comparable rate when meeting any further gates. (This might be because the assigned phonetic category is part of the listener’s internal “schemata”.)

I hold that this model disposes of any necessity for the idea of "functional decussation" originally used  to explain the experimental findings on auditory lateral advantage. That idea is unnecessarily committal on the underlying neurophysiology (see my manuscript abstracted in Social and Behavioral Sciences Documents 17, 43-44). For a bibliography of over 200 titles in journals relevant to the model see Cortex 25.