Sonority of 'h'?

I was trying to make up an interesting phonology using minimum sonority
distance (hoping that this would finally be the thing that led to a
*natural*-sounding artificial phonology), when the question of where to
put 'h' came up.

Does 'h' fit into the usual set of sonority classes?  In English it seems
like it can only appear as the sole onset of a syllable.  In Mohawk they
throw it around all over the place indiscriminately - does Mohawk use
sonority distance?  It seems that 'h' is treated in widely varying ways
by different languages.  Where does it fit?

Amanda

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