find mins/maxes with several conditions (similar to averageifs)

I've seen a few threads describing how to create your own MINIF function, but none that address the situation where several conditions need to be met (MINIFS). I want my formula to search a different sheet, 'Soil Results,' and calculate the smallest of the set where column D says '1', column G says 'subsurface soil,' and column I says 'cadmium.' The numbers I want to look at are in column J. I'm currently trying to use an and statement nested inside an if statement, but I think I must have the syntax wrong somewhere. I have the following formula, which is just returning 0. Any help would be greatly appreciated!

=MIN(IF(AND('Soil Results'!D2:D2761="1",'Soil Results'!G2:G2761="subsurface soil",'Soil Results'!I2:I2761="Cadmium"),'Soil Results'!J2:J2761,5))