Triggered by the first answer I got I wrote some more test code.
Before calling Serial.print I collected millis1. After the Serial.print was done I collected millis2. If (millis2 - mills1) was greater than 1 I sent a Serial.print of (millis2 - millis1). Sometimes I got a "2", regardless of Printing 5 or 25 characters.
Obviously interrupts are used. Asking for faster printout seems to be too much.
Going deeper, digging into source codes is more than I am prepared to do, Test and accept what I get, and use that is my idea,
Thanks guys!