Some listeners with hearing loss show poor speech recognition scores in spite of using amplification that optimizes audibility. Beyond audibility, studies have suggested that suprathreshold abilities such as spectral and temporal processing may explain differences in amplified speech recognition scores. A variety of different methods has been used to measure spectral processing. However, the relationship between spectral processing and speech recognition is still inconclusive. This study evaluated the relationship between spectral processing and speech recognition in listeners with normal hearing and with hearing loss. Narrowband spectral resolution was assessed using auditory filter bandwidths estimated from simultaneous notched-noise masking. Broadband spectral processing was measured using the spectral ripple discrimination (SRD) task and the spectral ripple depth detection (SMD) task. Three different measures were used to assess unamplified and amplified speech recognition in quiet and noise. Stepwise multiple linear regression revealed that SMD at 2.0 cycles per octave (cpo) significantly predicted speech scores for amplified and unamplified speech in quiet and noise. Commonality analyses revealed that SMD at 2.0 cpo combined with SRD and equivalent rectangular bandwidth measures to explain most of the variance captured by the regression model. Results suggest that SMD and SRD may be promising clinical tools for diagnostic evaluation and predicting amplification outcomes.