Makefiles question... $(OBJECT_FILES): $(HEADER_FILES)

Another newbie question which I haven't been able to figure out from the 
manual... again, apologies if this is basic.

I can write
$(LIST_OF_OBJECT_FILES): Header1.h Header2.h Header3.h

and I can write
Object1.obj: $(LIST_OF_HEADER_FILES)

but it seems I can't write
$(LIST_OF_OBJECT_FILES): $(LIST_OF_HEADER_FILES)

nor can I figure out a way of doing this indirectly, e.g. along the lines of
$(LIST_OF_OBJECT_FILES): all_headers
all_headers: $(LIST_OF_HEADER_FILES)

...the idea being to define some intermediate target. Am I trying to do 
something fundamentally impossible? (I.e. effectively 'pairing off' a pair 
of macros in every permutation?)

Thanks in advance!
Andy