This paper presents an efficient constant-time bilateral filter where constant-time means that computational complexity is independent of filter window size. Many state-of-the-art constant-time methods approximate the original bilateral filter by an appropriate combination of a series of convolutions. It is important for this framework to optimize the performance tradeoff between approximate accuracy and the number of convolutions. The proposed method achieves the optimal performance tradeoff in a least-squares manner by using spectral decomposition under the assumption that images consist of discrete intensities such as 8-bit images. This approach is essentially applicable to arbitrary range kernel. Experiments show that the proposed method outperforms state-of-the-art methods in terms of both computational complexity and approximate accuracy.