In this paper, we propose low-complexity lattice detection algorithms for successive interference cancelation (SIC) in multi-input multi-output (MIMO) communications. First, we present a dual-lattice view of the vertical Bell Labs Layered Space-Time (V-BLAST) detection. We show that V-BLAST ordering is equivalent to applying sorted QR decomposition to the dual basis, or equivalently, applying sorted Cholesky decomposition to the associated Gram matrix. This new view results in lower detection complexity and allows simultaneous ordering and detection. Second, we propose a partial reduction algorithm that only performs lattice reduction for the last several, weak substreams, whose implementation is also facilitated by the dual-lattice view. By tuning the block size of the partial reduction (hence the complexity), it can achieve a variable diversity order, hence offering a graceful tradeoff between performance and complexity for SIC-based MIMO detection. Numerical results are presented to compare the computational costs and to verify the achieved diversity order.