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We reexamine large CP-violating phases in the general Minimal SupersymmetricStandard Model, as well as more restricted models. We perform a detailed scanover parameter space to find solutions which satisfy the current experimentallimits on the electric dipole moments of the electron, neutron and $^{199}$Hgatom, exploring the allowed configurations of phases and masses, and we attemptto quantify the level of tuning of the parameters necessary to populate theregions of cancellations. We then consider the measurement of CP-violatingphases at a future linear collider. We find that measurements of chargino andneutralino masses and production cross-sections allow for a determination of$\phi_1$(the phase of $M_1$) to a precision of $\pi/30$, while the EDMconstraints require that $\theta_\mu$ be too small to be measured. Using theEDM constraints we find that the CP-even model parameters and the phase$\phi_1$ can be determined at a Linear Collider with $400 \gev$ c.m. energy. Aslong as some information on the size of $|\mu|$ is included in the observables,a measurement of $\phi_1$ is guaranteed for $\phi_1 > \pi/10$. To unambiguouslyidentify CP violation, we construct CP-odd kinematical variables at a linearcollider. However, the CP asymmetries are rather small, typically about$0.1-1.5%$, and it will be challenging to experimentally observe the predictedasymmetries.Comment: 29 pages, version accepted by PRD, Figure 8 changed, minor changes in  wordin

CP-violating phases in supersymmetry, electric dipole moments, and linear colliders