Tightbeam has a fairly rich history. Its current name was picked by its third editor, Marion Zimmer Bradley, in 1960 - and stuck.

In 1949, Art Rapp, the editor of Spacewarp, a popular fanzine, decided to put out a letterzine for the N3F, calling it Postwarp. This was available on subscription, at 10 cents a copy (the usual price in those days) which paid for itself. It contained letters on all subjects, but mainly discussed the N3F, and not being official, could be free to criticize (as continues to this day, even when edited by the President). When Art left, others took up Postwarp, with varying success, continuing to 1960, when Alan J. Lewis (not to be confused with Albert J. Lewis) has problems and Postwarp did not appear regularly or on time.

By now the zine was financed by the N3F, and the officers, understandably, wanted it to appear before they paid for it. Lewis, on the other hand, could not promise anything and claimed he needed the money in advance. This impasse went on for some time, and caused various new rules to be made, to no avail, so they decided to go around the delinquent editor by doing another letterzine, letting him delay Postwarp as long as he pleased. So, in a sense, Postwarp and Tightbeam (which was not quite the name of the new zine) were not related.

Walter Coslet volunteered to do the first issue, and named it Hyperspace Tightbeam. Another reliable, Art Hayes, did the next and Marion Zimmer Bradley (no less) edited the third issue, and promptly renamed it Tightbeam, a more sensible name which described the activity - that of serving as a medium for inter-member communication. So the first few editors rotated, setting a precedent, though sometimes it was more efficient to have a semi-permanent editor, who could control the contents of the issue to fit the pages allowed.