As stated, compact is going in the wrong direction if you want lower gears. 34 tooth instead of 30 (presumably) tooth smallest ring. To get lower gearing, you can get either a cassette with larger cogs, or a smaller granny ring, or both. You would likely need a new rear derailleur to handle larger max cog + more wrap (mountain bike *9-speed*, even though your bike is 10-speed, because Shimano's MTB 10-speed derailleurs use a different amount of cable pull than is compatible with road STI), and a new chain. For parts cost, shopping online, about $25 for a chain, $45-$65 for a rear derailleur, $30-$60 for a cassette.