The invention is an embolic coil having a complex secondary shape based on extensions of the coil into planes orthogonal to the length of the coil. A spring coil is wound on a secondary shaping mandrel having branched extensions positioned sequentially along the length of the linear base mandrel. The spring coil is wound around the base mandrel and the branches that extend or protrude from the base in successive increments creating coil extensions. The secondary wind is stress-relieved. The resulting occupation of space by the secondary shape of the embolic coil is space-filling with extensions into two or more planes, the extensions alternating along the length of the somewhat compressed coil. The invention allows a spring coil to act like a compression coil in its secondary shape.