  Much evidence suggests that the solar corona is heated impulsively, meaning
that nanoflares may be ubiquitous in quiet and active regions (ARs). Hard X-ray
(HXR) observations with unprecedented sensitivity $>$3~keV are now enabled by
focusing instruments. We analyzed data from the \textit{Focusing Optics X-ray
Solar Imager (FOXSI)} rocket and the \textit{Nuclear Spectroscopic Telescope
Array (NuSTAR)} spacecraft to constrain properties of AR nanoflares simulated
by the EBTEL field-line-averaged hydrodynamics code. We generated model X-ray
spectra by computing differential emission measures for homogeneous nanoflare
sequences with heating amplitudes $H_0$, durations $\tau$, delay times between
events $t_N$, and filling factors $f$. The single quiescent AR observed by
\textit{FOXSI-2} on 2014 December 11 is well fit by nanoflare sequences with
heating amplitudes 0.02 erg cm$^{-3}$ s$^{-1}$ $<$ $H_0$ $<$ 13 erg cm$^{-3}$
s$^{-1}$ and a wide range of delay times and durations. We exclude delays
between events shorter than $\sim$900 s at the 90\% confidence level for this
region. Three of five regions observed by {\nustar} on 2014 November 1 are well
fit by homogeneous nanoflare models, while two regions with higher fluxes are
not. Generally, the {\nustar} count spectra are well fit by nanoflare sequences
with smaller heating amplitudes, shorter delays, and shorter durations than the
allowed \textit{FOXSI-2} models. These apparent discrepancies are likely due to
differences in spectral coverage between the two instruments and intrinsic
differences among the regions. Steady heating ($t_N$ = $\tau$) was ruled out
with $>$99\% confidence for all regions observed by either instrument.
