According to Wikipedia's article on the Eblaite language:
Studying the usage context for the symbols I, I2, A, ʾA, ḪA, etc. with regard to the writing conventions of Akkadian scribes enabled the determination, beyond some identification difficulties created by the graphical barrier, of "the existence and autonomy of the phonemes /h/, /ḥ/, and /ḫ/ confirmed by the realization of the vowel /a/ as [ɛ] in the closed syllables /ḥaC/ and /ʾaC/, as well as the tendency to extend this phenomenon to the vowel /a/ followed by a pharyngeal. It is currently lacking the elements to determine the existence of a phoneme /ġ/ or a variant [ġ]."
Also through a contextual analysis of the symbols z + Vowel (V): ze2, s + V: se11, š + V, Pelio Fronzaroli confirmed the existence of the phonemes /s/, /ṣ/, /ḍ/, and /ẓ/, as well as the phonemes /s/, /š/, and /ṯ/, a group to which it is perhaps also necessary to add /z/.
I find this intriguing, and am curious to know more (for example, what alternate readings should we assign to these signs based on this, and what can this tell us about Sumerian?).
However, I haven't been able to find a good overview of Eblaite cuneiform; it usually seems to be mentioned as a sort of afterthought attached to Akkadian, with the writing system summarized as "we really don't know enough to say". Wikipedia cites Fronzaroli 1978 and 1980, but unfortunately I don't speak French well enough to understand technical works.
Where can I read more about this, preferably in English? Alternately, what is the state of the art here, if it can be summed up in the span of an answer?