This work refines the definition of the excess distortion exponent, used to measure the asymptotic finite block-length behavior of lossy source and joint source-channel coding. A distinction is made between the processing block of the coding scheme, the observation block of the user and, when applicable, the channel constraint block. While the length of the first block governs delay (and may be connected to complexity issues as well), the significance of the other lengths is different, and depends upon the application. Examples are shown, where relaxing the observation and channel-constraint requirements enables improving the processing-block exponent beyond the known upper bounds of the excess distortion exponent in its traditional form. As a by-product of the techniques used, we also find the yet-unknown ``traditional'' excess distortion exponent for some joint source-channel quadratic-Gaussian scenarios.