High-performance computing (HPC) systems that run scientific simulations of significance produce a large amount of data during runtime. Transferring or storing such big datasets causes a severe I/O bottleneck and a considerable storage burden. Applying compression techniques, particularly lossy compressors, can reduce the size of the data and mitigate such overheads. Unlike lossless compression algorithms, error-controlled lossy compressors could significantly reduce the data size while respecting the user-defined error bound. DCTZ is one of the transform-based lossy compressors with a highly efficient encoding and purpose-built error control mechanism that accomplishes high compression ratios with high data fidelity. However, since DCTZ quantizes the DCT coefficients in the frequency domain, it may only partially control the relative error bound defined by the user. In this paper, we aim to improve the compression quality of DCTZ. Specifically, we propose a preconditioning method based on level offsetting and scaling to control the magnitude of input of the DCTZ framework, thereby enforcing stricter error bounds. We evaluate the performance of our method in terms of compression ratio and rate distortion with real-world HPC datasets. Our experimental result shows that our method can achieve a higher compression ratio than other state-of-the-art lossy compressors with a tighter error bound while precisely guaranteeing the user-defined error bound.