The pitch strength of rippled noise and iterated rippled noise has recently been fitted by an exponential function of the height of the first peak in the normalized autocorrelation function [Yost, J. Acoust. Soc. Am. 100, 3329-3335 (1996)]. The current study compares the pitch strengths and autocorrelation functions of rippled noise (RN) and another regular-interval noise, "AABB." RN is generated by delaying a copy of a noise sample and adding it to the undelayed version. AABB with the same pitch is generated by taking a sample of noise (A) with the same duration as the RN delay and repeating it to produce AA, and then concatenating many of these once-repeated sequences to produce AABBCCDD.... The height of the first peak (h1) in the normalized autocorrelation function of AABB is 0.5, identical to that of RN. The current experiments show the following: (1) AABB and RN can be discriminated when the pitch is less than about 250 Hz. (2) For these low pitches, the pitch strength of AABB is greater than that for RN whereas it is about the same for pitches above 250 Hz. (3) When RN is replaced by iterated rippled noise (IRN) adjusted to match the pitch strength of AABB, the two are no longer discriminable. The pitch-strength difference between AABB and RN below 250 Hz is explained in terms of a three-stage, running-autocorrelation model. It is suggested that temporal integration of pitch information is achieved in two stages separated by a nonlinearity. The first integration stage is implemented as running autocorrelation with a time constant of 1.5 ms. The second model stage is a nonlinear transformation. In the third model stage, the output of the nonlinear transformation is long-term averaged (second integration stage) to provide a measure of pitch strength. The model provides an excellent fit to the pitch-strength matching data over a wide range of pitches.