One of the best arguments for using miles instead of cash to book your flights is that the routing rules are so much more flexible for award travel. Many loyalty programs allow you to add connections, stopovers and open jaws to your itinerary — meaning you can combine multiple trips into a single award.Using miles is frustrating for many travelers due to limited availability, and these tricks can make that puzzle more complicated. Most airlines' search tools are designed to find simple round-trip awards. It will be your responsibility to find award availability and piece together the complete itinerary, which might then require calling an agent to book. But you should feel comfortable attempting these strategies knowing they are well within most programs' official rules.See: How to Book Your Next Award Flight Like a ProThe easiest way to visit more cities on a single trip is to add free layovers and stopovers. Stopovers are connections that exceed four hours on domestic itineraries or 24 hours on international itineraries. Anything shorter than that is a layover. You can have as many layovers as you want, and even leave the airport for a brief tour of the connecting destination. Some cities, such as Zurich, Hong Kong and Singapore, offer convenient transit options to the city center. Stopovers are more restricted, but you can spend several days or weeks in a city before you continue onward to your final destination.Each airline has its own rules for stopovers. For example, Alaska Airlines permits a stopover on one-way awards — even for domestic travel — but United Airlines only allows a single stopover for international travel booked as part of a round-trip itinerary. But in general, all carriers require that travel be complete within 330 days of the original booking date, and visa limits may apply for any international city you visit.Award travel is typically priced according to the geographic regions of your origin and destination, and going out of your way to make extra stops doesn't usually cost extra. Some carriers are particularly generous by, for example, allowing travel from North America to Asia via Europe. Combined with a stopover, that would allow someone in New York to add a free trip to Paris as part of an existing trip to Bangkok. Carriers tend to be more flexible with open jaws than stopovers. An open jaw refers to "returning" to a different city than the one you departed from. It can also mean returning from a different city than the one in which you arrived. It gets its name from the gap created when you draw the itinerary on a map: Instead of a closed loop, the angle looks like an open jaw. Assuming you want to return to your home airport, it's a great way to explore a destination by land without returning to the exact city where you started (a tour of Europe, for example).See: Cheap Ways to Travel to Europe on PointsCombining stopovers with an open jaw creates interesting opportunities. You're not necessarily required to use a free stopover at your destination. Some people instead choose to stop at their home airport — or depending on the award rules, another airport nearby. (They still get to fly home from their destination, except that in the context of this itinerary "home" is really just a stop on a longer return journey.)Imagine creating an open jaw itinerary to Asia. San Francisco is the origin, Shanghai is the destination, but you know you need to go travel New York a month later. That return journey from Shanghai can be arranged to include a stopover in San Francisco, moving the actual "return city" to New York. After returning from Shanghai to San Francisco, you can head home for a month before you go back to the airport and continue on to New York for the second journey at no extra cost.You would still need to book a one-way flight back home from New York to San Francisco, but many domestic fares are priced on a one-way basis anyway. You've saved half the cost of your future New York visit by planning ahead.Stopovers and open jaws create opportunities to nest one award ticket within another. Cities that see infrequent service, such as Siem Reap, Cambodia, may have limited or no service depending on the network of airline partners available. As a result, it might make more sense to book an additional ticket, either paying cash or as a second award.Consider a round-trip from San Francisco to Bali via Bangkok using miles from United Airlines. (You could be flying any of United's partners and making additional connections as needed.) Bali is the destination, but Bangkok can be added as your one free stopover. Now you've got a chance to visit two destinations for the price of one. You can add a third destination by booking a round-trip fare on a discount carrier — in this case, Bangkok Airways from Bangkok to Siem Reap. In this scenario, you would fly to Bangkok, see the sights, and return to the airport. But you would fly to Siem Reap on a different ticket before flying back to Bangkok and continuing the original journey to Bali.These tricks don't work on every airline. American Airlines recently changed its rules to prohibit stopovers even though their policies weren't very generous to begin with. British Airways prices its awards separately for every individual segment, so it's impossible to game the system.For the programs that allow it, however, such rules can add exceptional value to your frequent flier miles. It's not as simple as saying that one program charges more miles than another for a given award. Sometimes a few extra miles are well worth the added flexibility in deciding where you stop along the way.See: The Best Airline Rewards Programs of 2014-15About the author: Scott Mackenzie is a neuroscientist who learned how to travel and earn elite status on the cheap during graduate school. He now shares these tricks on the blog Travel Codex. You can also follow him on Twitter @Travel_Codex.