We demonstrate that the peak-to-background ratio of driven solitons can be greatly improved by harnessing the cavity detuning. We use a driven fiber laser pumped below the lasing threshold to increase the finesse and excite solitons in a very wide range of detuning δ. When driving a 50 m long fiber cavity close to the anti-resonance condition (δ = π), we excite sub-800 fs solitons with a peak-to-background ratio close to 30 000. The experimental results are in good agreement with simple theoretical models describing the soliton peak power and the background power.