A spinal plate system comprising: a screw (400, 1900, 2306) including a head (402, 1902) and a threaded body (424, 1924); a spinal plate (100, 1100, 2600) including an opening (104-114, 1104, 1116) through the spinal plate and an associated recess (202, 1106, 1120, 2602) in the spinal plate that is eccentric with the opening (104-114, 1104, 1116); and a cap (500, 1300, 2300, 2700) including an alignment opening (508, 1310, 2702, 2704), the cap configured to be rotationally engaged in the recess (202, 1106, 1120, 2602) between a first rotational configuration and a second rotational configuration, wherein in the first rotational configuration the threaded body (424, 1924) of the screw is threadable into the vertebra in a selected trajectory through the alignment opening (508, 1310, 2702, 2704) and the opening (104-114, 1104, 1116) in the spinal plate (100, 1100, 2600) such that the head (402, 1902) engages at least a portion of the opening (104-114, 1104, 1116) in the selected trajectory, characterized in that: the head of the screw includes a portion of a first sphere (404, 1904) that has a first center and a portion of a second sphere (420, 1920) that has a second center, the second center being approximately concentric with the first center, the body extending from the portion of the first sphere; and in the second rotational configuration the cap (500, 1300, 2300, 2700) compresses the portion of the second sphere (420, 1920) into the portion of the first sphere (404, 1904) approximately through the first center of the first sphere such that the head (402, 1902) is compressed into the engaged portion of the opening (104-114, 1104, 1116). a screw (400, 1900, 2306) including a head (402, 1902) and a threaded body (424, 1924); a spinal plate (100, 1100, 2600) including an opening (104-114, 1104, 1116) through the spinal plate and an associated recess (202, 1106, 1120, 2602) in the spinal plate that is eccentric with the opening (104-114, 1104, 1116); and a cap (500, 1300, 2300, 2700) including an alignment opening (508, 1310, 2702, 2704), the cap configured to be rotationally engaged in the recess (202, 1106, 1120, 2602) between a first rotational configuration and a second rotational configuration, wherein in the first rotational configuration the threaded body (424, 1924) of the screw is threadable into the vertebra in a selected trajectory through the alignment opening (508, 1310, 2702, 2704) and the opening (104-114, 1104, 1116) in the spinal plate (100, 1100, 2600) such that the head (402, 1902) engages at least a portion of the opening (104-114, 1104, 1116) in the selected trajectory, the head of the screw includes a portion of a first sphere (404, 1904) that has a first center and a portion of a second sphere (420, 1920) that has a second center, the second center being approximately concentric with the first center, the body extending from the portion of the first sphere; and in the second rotational configuration the cap (500, 1300, 2300, 2700) compresses the portion of the second sphere (420, 1920) into the portion of the first sphere (404, 1904) approximately through the first center of the first sphere such that the head (402, 1902) is compressed into the engaged portion of the opening (104-114, 1104, 1116).