We show how the study of variations in orientation of a terrestrial reference system (TRS) in space may be done directly in terms of the motion of the pole of the TRS and rotation around it, and how a separation of these variations into low frequency and high frequency (retrograde and prograde diurnal, semidiurnal, · · · ) bands enables one to characterize and model variations belonging to the various bands and to estimate them simultaneously from observational data by a uniform procedure. Introduction of the Celestial Ephemeris Pole (CEP) or other Celestial Intermediate Pole (IP) is not only unnecessary, but also gives rise to needless debate as to whether variations due to particular causes are to be included in the celestial motion of the IP or in its terrestrial motion, and leaves the question of estimation of high-frequency signals in either frame unresolved. In regard to UT1, we point out that the “correction terms” through which the concept of the nonrotating origin is implemented emerge naturally from fundamental kinematical relations, and use this observation to identify the correction terms to be employed when the Earth orientation parameters are defined in relation to the pole of the TRS rather than an IP.