I have a query of the form:
select m.id from mytable m
left outer join othertable o on o.m_id = m.id
and o.col1 is not null and o.col2 is not null and o.col3
A partial index seems the right way here:
If you have a table that contains both billed and unbilled orders, where the unbilled orders take up a small fraction of the total table and yet those are the most-accessed rows, you can improve performance by creating an index on just the unbilled rows.
Perhaps those nullable columns (col1,col2,col3) act in your scenario as some kind of flag to distinguish some subclass of records in your table? (for example, some sort of "logical deletion") ? In that case, besides the partial index solution, you might prefer to rethink your design, and put them in different physical tables (perhaps using inheritance), one for the "live records" other for the "historical records" and access the full set (only when needed) thrugh a view.