After writing some FunctorM instance for GHC-6.4, then converting them to Traversable instances for GHC-6.8, I found that most of the time, if not always, I actually needed a FunctorM instance (i.e. fmapM method), not a Traversable instance. Defining a Traversable instance requires me to also define a Foldable instance, i.e. a foldMap function. I had trees, lists and singletons extended by additional information, e.g. data PositionList a = PositionList [(Position, a)] data AsyncException e a = AsyncException (Maybe e) a However 'foldMap' cannot utilize the additional information, namely Position and (Maybe e), respectively. In the first case this is sad, in the second case I consider this bad, since it is too easy to throw away and thus ignore the exception (Maybe e). Some kind of fold is always useful on these structures, but 'foldMap' is too limited. For Traversable there is always both sequence and mapM (and their Applicative counterparts), although you need to define only one of them. However 'sequence' works on interim data structures that are not very natural. Imagine a data structure with a 'string' parameter that is intended for instantiation by String or ByteString. Now 'sequence' requires instantiations like (IO String) or (State s ByteString) which do not share common properties of String and ByteString, e.g. having a 'length' function. Although possible, those interim types look inappropriate to me. Even more, consider a data structure like StorableVector which requires certain properties of its elements. StorableVector is intended for Int, Double and other Storable types, but you cannot store (IO Double) values. This example is not practical, because the Storable restriction disallows to define both Traversable and FunctorM instances. However you see, that one cannot even imagine 'sequence' on StorableVector, whereas 'mapM' is possible, yet very inefficient (needs copying the entire vector for each added element). My conclusion is, that FunctorM was better than its reputation, and that Traversable as it is, is not what I need most of the time. What are the experiences of other Traversable users?