excluding records from the resultset based on two criteria

I am looking for the best (fastest/less-resource-intensive) way to compare two mysql query resultsets (or even arrays) and remove or ignore records from one that exist in another. The catch is that the exclusion of records from the master resultset which exist in the secondary resultset must be based on two keys. I will illustrate below:
TABLE MASTER
--num1-- --num2--
1             3
1             6
2             5
3             4
3             8
3             16

TABLE MINOR
--num1-- --num2--
1              3
3              8

If this were a simple task of determining which records in the MASTER table did not exist in the MINOR table based on one key then the following query (as one method) would work:
SELECT num1, num2 FROM MASTER WHERE num1 NOT IN (SELECT num1 FROM MINOR);

However, I want to omit records from MASTER where num1 AND its associated num2 value appear in the MINOR table. For example, the desired dataset would look like:
RESULTS AFTER COMPARE
--num1-- --num2--
1             6
2             5
3             4
3             16

Currently I am having to run one query to pull results from the MASTER table, then run another query to get results from the MINOR query, then loop through the resultsets to compare the num1 AND num2 values. While this works, it is very slow, especially when dealing with large datasets. Any ideas?