Calculations of the properties of rotating strange stars with crusts are pe
rformed within the framework of general relativity. We employ an equation o
f state (EOS) of strange quark matter based on the MIT Bag Model with massi
ve strange quarks and lowest order QCD interactions. The crust is described
by the BPS equation of state. A significant increase of the stellar radius
is found close to the Keplerian (mass-shedding limit) configuration. This
leads to the disappearance of the gap between the stellar surface and the i
nnermost stable circular orbit (ISCO) at very high rotation rates, for a ra
ther broad range of stellar masses. The Keplerian configuration for the str
ange star with crust corresponds to values of J, T/W, PISCO = 1/v(ISCO) whi
ch are about 20% smaller than in the case of bare strange stars. Because th
e Keplerian configuration is achieved due to the increase of the stellar ob
lateness, the Keplerian frequency (of the rotation) remains almost unaltere
d. The lack of the gap close to the Keplerian rotation could imply a more s
tringent limit on v(ISCO), if the existence of such a gap is supported by o
bservations, as in the source 4U 1820-30 with the upper QPO frequency 1.07
kHz. If such a constraint is taken into account (mandatory existence of a g
ap) the minimum v(ISCO) is about 1 kHz even with the extreme fine tuning of
strange quark matter parameters. The minimum v(ISCO) is then obtained for
the non-rotating configuration with maximum allowable mass. The maximum fre
quency in the stable circular orbit around the strange star with a crust is
smaller by about 100 Hz than in the case of a bare strange star. During th
e spin-down of a magnetized strange quark star with crust, the crust matter
is absorbed in the equatorial region by the strange matter core. The decon
finement of absorbed crust matter is a strongly exothermic process, which w
ould influence the cooling curve of this compact object.