This paper presents an extension to the Conservative PC algorithm which is able to detect violations of adjacency faithfulness under causal sufficiency and triangle faithfulness. Violations can be characterized by pseudo-independent relations and equivalent edges, both generating a pattern of conditional independencies that cannot be modeled faithfully. Both cases lead to uncertainty about specific parts of the skeleton of the causal graph. This is modeled by an f-pattern. We proved that our Very Conservative PC algorithm is able to correctly learn the f-pattern. We argue that the solution also applies for the finite sample case if we accept that only strong edges can be identified. Experiments based on simulations show that the rate of false edge removals is significantly reduced, at the expense of uncertainty on the skeleton and a higher sensitivity for accidental correlations.