The act of speaking excessively or continuously is referred to as verbal diarrhea. How about speaking very little? Is there a word for it?
If you need a (possibly periphrastic) term with negative nuance then verbal constipation sounds appropriate.
An opposite term though of verbal diarrhea, which most often is used as a virtue is laconicism. (From the greek word λακωνικός=laconic, which originates from Laconia, the ancient greek state with capital Sparta, where it was considered a virtue to express yourself using a mimimal amount of words.)
A good term to describe the person who speaks little (as opposed to the act itself of remaining silent) is taciturn.
Many other words that describe people who tend to be quiet imply their reasons for not being talkative--for instance, reticent, diffident, and aloof. Taciturn has relatively little nuance in that respect.
As John says, verbal constipation would seem suitable (and witty). More fun, but sadly less suitable, might be verbal charley horse.
"Succinct": using few words to state or express an idea