ignores covering index

I have a common search query on a simple table that has only a single covering (nonclustered, not unique) index.

This will use the index:

SELECT @bOK = 1 
FROM verify_e1_account		
WHERE 
  (e1_business_unit = @p_e1_business_unit)
  AND (e1_gl_acct = @p_e1_gl_acct)
  AND (e1_cost_code = @p_e1_cost_code));

This will not use the index, but it looks to me like it should:

SELECT @bOK = 1 
FROM verify_e1_account		
WHERE 
  (@p_e1_business_unit IS NULL OR e1_business_unit = @p_e1_business_unit)
  AND (@p_e1_gl_acct IS NULL OR e1_gl_acct = @p_e1_gl_acct)
  AND (@p_e1_cost_code IS NULL OR e1_cost_code = @p_e1_cost_code);

How can I make the second version use the index?

Table has a million rows, but all levels are selective.

For a given value, just specifying the business unit returns only 239 rows, specifying both business unit and gl_acct cuts that down to 2 rows.  Apparently the optimizer can't see that.

In case it matters, the table is a heap, the covering index is not clustered, there is no clustered index.

Adding separate indexes (and thus statistics) on the separate fields does not fix it, whether or not I also drop the covering index.  Fields are char(6),char(8),char(12).

I'd like to understand this, as much as fix it.

SQL Server 2008 SP1 Standard 64-bit.

Thanks,

Josh