The abundance of online data is at risk of unauthorized usage in training deep learning models. To counter this, various Data Availability Attacks (DAAs) have been devised to make data unlearnable for such models by subtly perturbing the training data. However, existing methods often excel in either Supervised Learning (SL) or Self-Supervised Learning (SSL) scenarios. Among these, a model-free approach that generates a Convolution-based Unlearnable Dataset (CUDA) stands out as the most robust DAAs across both SSL and SL. Nonetheless, CUDA's effectiveness on SSL remains inadequate and it faces a trade-off between image quality and its poisoning effect. In this paper, we conduct a theoretical analysis of CUDA, uncovering the sub-optimal gradients it introduces and elucidating the strategy it employs to induce class-wise bias for data poisoning. Building on this, we propose a novel poisoning method named Imperfect Restoration Poisoning (IRP), aiming to preserve high image quality while achieving strong poisoning effects. Through extensive comparisons of IRP with eight baselines across SL and SSL, coupled with evaluations alongside five representative defense methods, we showcase the superiority of IRP.