The negative structural design of RNAs, also called Inverse folding, consists in building a synthetic nucleotides sequence adopting a targeted secondary structure as its Minimum Free Energy (MFE) structure. Computationally an NP hard problem, it is mostly addressed as an optimization task and solved using (meta-)heuristics. Existing methods are frequently challenged by demanding instances, and typically produce a single design, hindering practical applications of design, where multiple candidates are desirable to circumvent the idealized nature of design models. In this work, we introduce RNA POsitive and Negative Design (RNAPOND), a sampling approach which generates design candidates exactly from a well-defined distribution influenced by positive design objectives, including affinity towards the target and GC-content. Negative design principles are captured by an original iterative approach, where a subset of Disruptive Base Pairs (DPBs) are identified at each step, and subsequently forbidden from pairing by the introduction of suitable constraints. Despite the NP-hardness of the associated decision problem, we propose a combinatorial sampling algorithm which is Fixed Parameter Tractable (FPT) for the tree-width of the constraint network. Our algorithm, coupled with a suitable rejection step and an automated inference of DPBs, achieves a similar or better level of success in comparison to the state of the art, while allowing for the generation of diverse designs. Interestingly, it also automatically recovers some of the strategies used by practitioners of RNA design. RNAPOND is an open source project, available at: https://gitlab.inria.fr/amibio/RNAPOND