Pressure of speech refers to rapid, frenzied and often cluttered fashion of speech. There is usually an underlying psychological disorder and that disorder would need to be treated to relieve the pressure of speech.

” “Pressure of speech’ is a hallmark of mania and is often seen during manic periods in patients with bipolar disorder. The pace of the speech indicates an underlying thought disorder known as “flight of ideas” where the information going through the person’s head is so fast that it is difficult to follow his train of thought.”

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I have never heard the term, but would assume it meant the weight (impact) of the message delivered.

@kritiper: No, it means what the first two responses say it means.

http://medical-dictionary.thefreedictionary.com/logorrhea

Logorrhea: Pressured speech medical definition above.