Are staircases more efficient than the method of constant stimuli? 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 [1] 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. 
  




[1] Klein, S. A. (2001). Measuring, estimating, and understanding the psychometric function: a commentary. Perception &amp; Psychophysics, 63(8), 1421–55. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/11800466