A Bayesian Quest adaptive procedure (Watson and Pelli 1983) is the theoretically most efficient procedure for estimating thresholds under a certain, potentially unrealistic, set of constraints. In my field a transformed up-down method (Levitt 1971) is used much more commonly. Has any work been done comparing the efficiency of the transformed up-down method with the method of constant stimuli?
There was a special issue of the journal Perception and Psychophysics in 2001, titled Psychometric Functions and Adaptive Methods. It contains several papers relevant to your question. Klein's paper  references all the others and reviews what each is about. It should serve as a good starting point.
An excerpt from Klein's summary:
- The simple up–down (Brownian) staircase with threshold estimated by averaging levels was found to have nearly optimal efficiency in agreement with Green (1990). It is better to average all levels (after about four reversals of initial trials are thrown out) rather than average an even number of reversals.Both of these findings were surprising.
- As long as the starting point is not too distant from threshold, Brownian staircases with their moderate inertia have advantages over the more prestigious adaptive likelihood methods. At the beginning of a run, likelihood methods may have too little inertia and can jump to low stimulus strengths before the observer is fully familiar with the test target. At the end of the run, likelihood methods may have too much inertia and resist changing levels even though a non stationary threshold has shifted.
 Klein, S. A. (2001). Measuring, estimating, and understanding the psychometric function: a commentary. Perception & Psychophysics, 63(8), 1421–55. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/11800466