In volume-rendering applications, it is a de facto standard to reconstruct the underlying continuous function by using trilinear interpolation, and to estimate the gradients for the shading computations by calculating central differences on the fly. In a GPU implementation, this requires seven trilinear texture samples: one for the function reconstruction, and six for the gradient estimation. In this paper, for the first time, we show that the six additional samples can be used not just for gradient estimation, but for significantly improving the quality of the function reconstruction as well. As the additional arithmetic operations can be performed in the shadow of the texture fetches, we can achieve this quality improvement for free without reducing the rendering performance at all. Therefore, our method can completely replace the standard trilinear interpolation in the practice of GPU-accelerated volume rendering.