The purpose of the study was to compare the differential effects of response independent and response-dependent criteria used to determine when to increase to the next delay interval in the progressive time delay (PTD) procedure. An adapted alternating treatments design was used to evaluate the relative efficiency of three variations of the PTD procedure when teaching expressive word identification to first-grade children with moderate to severe intellectual or developmental disabilities, language impairments, and reading deficits. All three PTD variations consisted of increasing the delay interval in 1-s increments from 0s to 4s. The three PTD variations compared included (a) a response-independent variation in which the delay interval was increased every session regardless of participant responding, (b) a response-dependent variation in which the delay interval was increased after the participant achieved 100% prompted or unprompted correct responses for one session, and (c) a second response-dependent variation in which the delay interval was increased after the participant achieved 100% prompted or unprompted correct responses for one session AND decreased to the previous delay interval in the next session following a session with at least one incorrect response. These three variations represent (a) one of the most common response-independent variations for increasing delay intervals, (b) one of the most common response-dependent variations for increasing delay intervals, and (c) one of the most common response-dependent variations for increasing delay intervals paired with one of the most common variations for decreasing delay intervals. Results obtained indicated that all variations were effective in increasing participants' percentage of unprompted correct responses when identifying sight words with generalized responding across instructors and across stimuli. Results pertaining to efficiency via acquisition rates were mixed; acquisition rates were either (a) relatively equal across PTD variations or (b) superior with response-dependent variations. Results pertaining to differentiation in the error rates of each variation indicated superiority with the response-dependent variations; both response dependent variations were more efficient in increasing independent performance with considerably fewer errors when compared to the response-independent variation. None of the variations were considerably more efficient in terms of the instructional time required to implement the procedures. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]