Where did the saying "sleep tight" come from?

I understand the "don't let the bedbugs bite" part of the age-old bedtime sentiment, but hadn't a clue why or how one is supposed to "sleep tight." We've learned from past experience that uncovering the origins of common expressions and words can be tricky -- it's rare that there is a clear-cut and widely agreed upon answer. A search on "sleep tight origin" quickly showed us that this familiar saying was no exception. The very first site listed in our search results was World Wide Words, a valuable resource we often consult when researching etymology. As web-site author and veteran word-hunter Michael Quinion explains, before the advent of modern mattresses, ropes were spread across the bed frame in a criss-cross pattern to form a sleeping platform. The ropes would sag with time and weight and had to be tightened periodically. While many believe that "sleep tight" sprung from this type of bed, Quinion casts some doubt on this seemingly logical explanation. He points out that the saying "sleep tight" appears to date back only as far as 1866 (the bedbug part of the saying is a more recent addition), while rope-frame beds date much further back and therefore seem an unlikely origin.
Some sites claim that the rope-frame bed explanation is "common knowledge" among historians, but we did find other sources that took issue with this theory. According to Wordorigins, another resource we regularly turn to with questions of this sort, one of the archaic definitions of "tight" was soundly. "Sleep tight" simply meant "sleep well."
Finally we checked in with Evan Morris, aka the Word Detective. He corroborated that "tight" was commonly used in the 18th and 19th centuries to mean "soundly." He furthers his argument by pointing out that the "suspended bed theory" is usually spouted by tour guides, who he states "constitute one of today's major 'vectors' or carriers of unfounded etymological 'urban legends.'"
When you put it like that, we'll have to side with our trusted and oft-cited sources and go with the dictionary theory.