The authors suggest a modified quadratic approximation scheme, and apply this scheme to American barrier (knock-out) and floating-strike lookback options. This modified scheme introduces an additional parameter into the quadratic approximation method, originally suggested by G. Barone-Adesi and R. Whaley (1987), to reduce pricing errors. When the barrier is close to the underlying asset's current price, the approximation formula is more accurate than lattice methods because the optimal exercise boundary is independent of the underlying asset's current price. That is, the proposed method overcomes the "near-barrier" problem that occurs in lattice methods. In addition, the pricing error decreases when the underlying asset's volatility is high. This approximation scheme is more efficient than B. Gao, J. Huang, and M. Subrahmanyam's (2000) method. As a second application of the modified approximation scheme, the authors provide an approximation formula for American floating-strike lookback options which is the first approximation formula ever suggested in the literature. Compared to S. Babbs'(2000) binomial approach, our approximation method is more efficient after controlling for pricing errors, and is more accurate after controlling for computing time. (c) 2007 Wiley Periodicals, Inc.