Temporal fine structure (TFS) is assumed to play an important role in both pitch and speech processing in normal hearing (NH). However, there is still some debate on how TFS is coded in the auditory periphery. Moore & Sek (2009, doi: 10.1121/1.3106525) provided evidence that NH subjects are sensitive to TFS at very high frequencies in stimulus conditions where spectral cues should not be present. This is important because it implies that phase locking may still provide useful information above 4000 Hz where it is commonly believed to be absent. Here, we examine sensitivity to TFS using different stimuli than the frequency-shifted complexes previously used. Pulse-spreading harmonic complexes (PSHCs) are spectrally-dense complexes with a low f0 (here 2 Hz). The phase of the components is set so that the envelope rate can be manipulated independently from the f0. Here, we use a special case of PSHCs for which the TFS peaks were shifted relative to the envelope peaks from one envelope period to the next. For upward PSHCs (up-PSHC), the TFS peaks were progressively advanced, yielding a rising pitch percept across the stimulus, while for downward PSHCs (down-PSHC), the peaks were progressively delayed, yielding a falling pitch percept. In Experiment 1, subjects heard up-PSHC, down-PSHC and regular inharmonic complexes bandpass-filtered with a lower cut-off (Fc) of 2000 Hz and were asked to identify whether the pitch was rising, falling or flat in a one interval, three alternative forced choice task. The envelope rate was 98, 200 or 450 pps. For the two highest rates, most subjects correctly identified the direction of the pitch change while for the lowest rate, the stimuli could not be discriminated. This shows that, for a given Fc, there is an envelope rate below which the auditory system is insensitive to changes in TFS. The lower rate limit of TFS sensitivity was measured in Experiment 2 using an adaptive three interval, two alternative forced choice task where subjects heard two down-PSHC and one up-PSHC and had to pick the latter. The stimuli were bandpass filtered in seven frequency regions with Fc varying from 250 to 11200 Hz and were presented in the presence of threshold-equalising noise. The lower limit significantly increased from 42 pps to 691 pps with increases in Fc. The ratio between Fc and the envelope rate at threshold also increased from 6 to 18 when Fc increased from 250 to 2000 Hz, then remained flat with further increases in Fc or slightly decreased at the highest Fc. In the lower part of the spectrum (<2000 Hz), this lower limit resembles the lower limit of melodic pitch. The results in the upper part of the spectrum suggest that TFS cues are still available in high frequency regions (up to 10 kHz) when the rank of the lowest harmonic present in the passband is 18, and all harmonics are presumably unresolved.