Auditory evoked potentials can be estimated by synchronous averaging when the responses to the individual stimuli are not overlapped. However, when the response duration exceeds the inter-stimulus interval, a deconvolution procedure is necessary to obtain the transient response. The iterative randomized stimulation and averaging and the equivalent randomized stimulation with least squares deconvolution have been proven to be flexible and efficient methods for deconvolving the evoked potentials, with minimum restrictions in the design of stimulation sequences. Recently, a latency-dependent filtering and down-sampling (LDFDS) methodology was proposed for optimal filtering and dimensionality reduction, which is particularly useful when the evoked potentials involve the complete auditory pathway response (i.e., from the cochlea to the auditory cortex). In this case, the number of samples required to accurately represent the evoked potentials can be reduced from several thousand (with conventional sampling) to around 120. In this article, we propose to perform the deconvolution in the reduced representation space defined by LDFDS and present the mathematical foundation of the subspace-constrained deconvolution. Under the assumption that the evoked response is appropriately represented in the reduced representation space, the proposed deconvolution provides an optimal least squares estimation of the evoked response. Additionally, the dimensionality reduction provides a substantial reduction of the computational cost associated with the deconvolution. matlab/Octave code implementing the proposed procedures is included as supplementary material.