Dielectric spectroscopy measurements over a broad range of temperature and pressure were carried out on poly(oxybutylene) (POB), a type A polymer (dielectrically active normal mode). There are three dynamic processes appearing at lower frequency: the normal and segmental relaxation modes and a conductivity arising from ionic impurities. In combination with pressure-volume-temperature measurements, the dielectric data were used to assess the respective roles of thermal energy and density in controlling the relaxation times and their variation with T and P. We find that the local segmental and the global relaxation times are both a single function of the product of the temperature times the specific volume, with the latter raised to the power of 2.65. The fact that this scaling exponent is the same for both modes indicates they are governed by the same local friction coefficient, an idea common to most models of polymer dynamics. Nevertheless, near T-g, their temperature dependences diverge. The magnitude of the scaling exponent reflects the relatively weak effect of density on the relaxation times. This is usual for polymers, as the intramolecular bonding, and thus interactions between directly bonded segments, are only weakly sensitive to pressure. This insensitivity also means that the chain end-to-end distance is invariant to P, conferring a near pressure independence of the (density-normalized) normal mode dielectric strength. The ionic conductivity dominates the low-frequency portion of the spectra. At lower temperatures and higher pressures, this conductivity becomes decoupled from the relaxation modes (different T dependence) and exhibits a significantly weaker density effect. At frequencies higher than the structural relaxation, both an excess wing on the flank of the alpha-peak and a secondary relaxation are observed. From their relative sensitivities to pressure, we ascribe the former to an unresolved Johari-Goldstein (JG) relaxation, while the higher frequency peak is unrelated to the glass transition. These designations are consistent with the relaxation time calculated for the JG process. The dynamic properties of the POB are essentially the same as those of poly(propylene glycol), in accord with their similar chemical structures. However, POB is less fragile (weaker T-g-normalized temperature dependence), its relaxation times are less sensitive to density changes, and, facilitating the measurements herein, its normal mode has a substantially larger dielectric strength.