We describe the deformed covariant phase space corresponding to the so-call
ed cc-deformation of D = 4 relativistic symmetries, with quantum "time" coo
rdinate and Heisenberg algebra being obtained according to the Heisenberg d
ouble construction. The associated modified uncertainty relations are analy
zed, and, in particular it is shown that these relations are consistent wit
h independent estimates of quantum-gravity limitations on the measurability
of spacetime distances.