netParcel (https://apps.shopify.com/netparcel) provides US domestic rates via FedEx. National shipping for items between 1-5 lbs across the country start at $8.
Our app also allow you to publish real time rates at checkout and import order for easy processing.
Please take a look and if you have any further questions, please email our support team email@example.com
What carrier are you currently using, how long have you been with them, and what is your daily volume?
You can usually negotiate lower rates with a direct competitor (UPS vs. FedEx), or by working with a third party provider as Derek mentioned. I'm happy to share some pricing insights/expectations based on the above info and can give you negotiation tips if you haven't already been through that process.
If you are new to shipping or have a small business, going with Shopify's default integration will save tons of money for you. The reason being Shopify provides heavily discounted rates for UPS, USPS, DHL. You can opt for it. Or else, opt for other resellers like Shipstation or netparcel. However, if you have some volume, a better way would be to get an account from any of these carriers thereby getting discounted rates and then using the account in the Multi Carrier Shipping label(MCSL) app to show rates to your customers at checkout.