  Speckle is the spatial fluctuation of irradiance seen when coherent light is
reflected from a rough surface. It is due to light reflected from the surface's
many nooks and crannies accumulating vastly-discrepant time delays, spanning
much more than an optical period, en route to an observation point. Although
speckle with continuous-wave (cw) illumination is well understood, the emerging
interest in non-line-of-sight (NLoS) imaging using coherent light has created
the need to understand the higher-order speckle that results from multiple
rough-surface reflections, viz., speckled speckle and speckled speckled
speckle. Moreover, the recent introduction of phasor-field
($\mathcal{P}$-field) NLoS imaging---which relies on amplitude-modulated
coherent illumination---requires pushing beyond cw scenarios for speckle and
higher-order speckle. In this paper, we take first steps in addressing the
foregoing needs using a three-diffuser transmissive geometry that is a proxy
for three-bounce NLoS imaging. In the small-diffusers limit, we show that the
irradiance variances of cw and modulated $n$th-order speckle coincide and are
$(2^n-1)$-times those of ordinary (first-order) speckle. The more important
case for NLoS imaging, however, involves extended diffuse reflectors. For our
transmissive geometry with extended diffusers, we treat third-order cw speckle
and first-order modulated speckle. Our results there imply that speckle is
unlikely to impede successful operation of coherent-illumination cw imagers,
and they suggest that the same might be true for $\mathcal{P}$-field imagers.
