You might enjoy "
Bakeneko," the final three-episode arc of
Ayakashi Samurai Horror Tales, and its sequel, the twelve-episode series
Mononoke. These form a collection of short stories about a "medicine seller" who also slays demons in the Edo period. Every story requires the protagonist to determine three characteristics of the demon in order to slay it. All the demons are conjured up by the malevolent acts of humans who must be interrogated to solve the mystery.
Another option might be
Mouryou no Hako, which starts off looking like a romance between two high-school girls, but quickly turns darker when one of them is hit by a train.
My first vote would be for
Monster as well.