While Amazon (AMZN) has made two-day and even two-hour order fulfillment a reality, it still faces a problem with shipping, along with every other retailer: It doesn’t control the “last mile” delivery to consumers, Loop Capital’s Anthony Chukumba and Rick Paterson write. Their solution: Buy FedEx (FDX).

The issue is that Amazon has to rely on third parties when it comes to delivery and returns, and Chuckumba and Paterson write that FedEx and UPS (UPS) naturally want to take “their pound of flesh” from the process, in this case in the form of margin.

Yet doing so, while a thorn in Amazon’s side, is becoming more important to UPS and FedEx, as business-to-consumer shipments, which are low margin, have reached a “critical mass,” that’s straining their margins and budgets–which hasn’t gone unnoticed by shareholders, who want price increases.

This is playing out agains a broader backdrop of inefficiencies in the system that make a deal more appealing:

Finally, there are also inherent cost inefficiencies in the broader system driven by the lack of coordination and competing interests between the sellers and shippers that could be eliminated by bringing them under one roof. Amazon’s options are to: 1) do nothing (unlikely); 2) build its own last mile network (drones are no silver bullet); or 3) buy. In this report we discuss all three options and focus on FedEx for the buy option, which we regard as the better fit.

That said, they don’t think that an Amazon bid for FedEx is probable in the near-term (or maybe even ever), given Amazon’s focus on expanding into international markets, developing AI via Alexa, and retooling its video strategy, but they think it’s “food for thought” as the company seeks new solutions for the last mile problem.

Amazon, FedEx, and UPS are all down about 0.3% in recent trading.