We present a novel method to optimize the attenuation of light for the single scattering model in direct volume rendering. A common problem of single scattering is the high dynamic range between lit and shadowed regions due to the exponential attenuation of light along a ray. Moreover, light is often attenuated too strong between a sample point and the camera, hampering the visibility of important features. Our algorithm employs an importance function to selectively illuminate important structures and make them visible from the camera. With the importance function, more light can be transmitted to the features of interest, while contextual structures cast shadows which provide visual cues for perception of depth. At the same time, more scattered light is transmitted from the sample point to the camera to improve the primary visibility of important features. We formulate a minimization problem that automatically determines the extinction along a view or shadow ray to obtain a good balance between sufficient transmittance and attenuation. In contrast to previous approaches, we do not require a computationally expensive solution of a global optimization, but instead provide a closed-form solution for each sampled extinction value along a view or shadow ray and thus achieve interactive performance.