The contralateral medial olivocochlear reflex (MOCR) strength may indicate various auditory conditions in humans, but a clinically viable assay and equipment are needed for quick, accurate, and reliable measurements. The first experiment compared an earlier version of the assay, which used a nonlinear-mode chirp stimulus, with a new assay using a linear-mode click stimulus, designed to give reliable MOCR measurements in most normal-hearing ears. The second experiment extended the improved assay on a purpose-built binaural hardware platform that used forward-pressure level (FPL) calibration for both the stimulus and the contralateral MOCR elicitor. Transient-evoked otoacoustic emission (TEOAE) tests were measured with and without a 60-dB SPL MOCR-evoking contralateral broadband noise. The normalized MOCR strength (MOCR%) was derived from the TEOAE responses for each trial pair using the complex pressure difference weighted by the TEOAE magnitude. Experiment 1 compared MOCR% within-subject and across-day using two TEOAE stimuli: nonlinear-mode chirps (50 dB SPL, bandpass 1-5 kHz, 14 ms window delayed by 2 ms) and linear-mode clicks (50 dB SPL, bandpass 0.5-2.5 kHz, 13 ms window delayed by 5 ms). TEOAE responses were analyzed in the 0.5 to 2.5 kHz band. Thirty adult participants with normal hearing (30 ears) completed the study. The TEOAE stimulus was calibrated in situ using spectral flattening, and the contralateral noise was calibrated in a coupler. Twelve TEOAE trial pairs were collected for each participant and condition. Experiment 2 used a purpose-built binaural system. The TEOAE stimuli were linear-mode clicks (50 dB SPL, bandpass 1-3 kHz, 13 ms window delayed by 5 ms), analyzed in the 1 to 3 kHz band over ~12 trial pairs. After a probe refit, an additional trial pair was collected for the two early-stopping signal-to-noise ratio criteria (15 and 20 dB). They were evaluated for single-trial reliability and test time. Nineteen adult participants with normal hearing (38 ears) completed the study. The TEOAE clicks and contralateral elicitor noise were calibrated in situ using FPL and delivered with automated timing. MOCR% for linear-mode clicks was distinguishable from measurement variability in 98% to 100% of participants' ears (both experiments), compared with only 73% for the nonlinear-mode chirp (experiment 1). MOCR detectability was assessed using the MOCR% across-subject/within-subject variance ratio. The ratio in experiment 1 for linear-mode clicks was higher (8.0) than for nonlinear-mode chirps (6.4). The ratio for linear-mode clicks (8.9) in experiment 2 was slightly higher than for the comparable linear-mode stimulus (8.0) in experiment 1. TEOAEs showed excellent reliability with high signal-to-noise ratios in both experiments, but reliability was higher for linear-mode clicks than nonlinear-mode chirps. MOCR reliability for the two stimuli was comparable. The FPL pressure response retest reliability derived from the SPL at the microphone was higher than the SPL retest reliability across 0.4 to 8 kHz. Stable results required 2 to 3 trial pairs for the linear-mode click (experiments 1 and 2) and three for the nonlinear-mode chirp (experiment 1), taking around 2 min on average. The linear-mode click assay produced measurable, reliable, and stable TEOAE and MOCR results on both hardware platforms in around 2 min per ear. The stimulus design and response window ensured that any stimulus artifact in linear mode was unlikely to confound the results. The refined assay is ready to produce high-quality data quickly for clinical and field studies to develop population norms, recognize diagnostic patterns, and determine risk profiles.