Tone/Pitch Accent Question

Hey all,

Various tone conventions have posited that the reality of tone is such that 
tone languages have tone melodies.   A common West African set of tone melodies 
is as follows: (1) H, (2) L, (3) HL, (4) LH, and (5) HLH.   What this means 
is that you can get words with only a 1, 2, 3, 4 or 5 melody, so, for example, 
never LHL.   When you get to trisyllabic words, however, it's unclear to me 
whether you can get:

HL pattern: háláme, or
HL pattern: hálame, or
Both.

I seem to recall that you can only get one, and if it was that way, it'd 
probably be the second, since you seem to associate tones right to left (though 
some languages can do left to right).   Either way, you can never get both.

Bearing that in mind, I've always assumed that pitch-accent languages work 
differently.   In pitch accent languages, you can have, maximally, 1-4 tone 
melodies (all high, all low, some high then all low, or some low then all high).   
You can never go from L to H to L, or from H to L to H (this is what I've 
been told).   Anyway, let's say, for the sake of argument, that in any given tone 
language, you can only have one of the above (two highs then a low, or one 
high then two lows, never both in the same language).   If that's true for a 
tone language, is it *not* true for a pitch-accent language?   In other words, 
could you get both in a pitch-accent languages?   I've assumed that you can.   
If you cannot, though, I'm going to have to radically rework one of my 
languages.

That's all.   :)   Any help is greatly appreciated.

-David

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