Many travelers think of low-fare carriers and rail passes as the smartest means for touring Europe. But in the same way that airlines offer last-minute deals to fill empty seats, Europe's rail networks have deeply discounted point-to-point tickets under promotional names like Smart Price and Bargain Berths. The tickets typically sell out quickly and may require Internet booking, though you're saved from the hassles (and costs) of getting to airports.

Offers are generally nonrefundable and valid only on the train you book (no changes). While availability is limited, bargains exist for travelers willing to search. Unless noted, the prices are for one-way tickets in second class.

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THE TRIP: ROME TO PARIS
Normal price: $220

Sale price: $45

Here's the Deal: Trenitalia's Smart Price ticket has a select few bargain fares on routes from Italy to nearby countries. A trip from Milan to Nice costs as little as $20. An overnight train from Rome to Paris, including a bed in a six-couchette compartment, starts at $45.

Booking Details: Advance-purchase requirements vary from 7 to 14 days depending on route. Buy at trenitalia.com and collect your ticket at a booth at the point of departure.

THE TRIP: MUNICH TO BERLIN
Normal price: $135

Sale price: $9

Here's the Deal: For $45, up to five people can split a single Schönes-Wochenende ("Happy Weekend") ticket and have unlimited rides anywhere in Germany on either a Saturday or Sunday. The offer, from Deutsche Bahn, isn't valid on the high-speed ICE, IC, and EC trains.

Booking Details: Tickets are sold at counters and machines in German train stations, with no advance purchase required. To plan an itinerary, go to bahn.de. Using the drop-down menu, search Without ICE/IC/EC and click on Prefer Fast Connections.

THE TRIP: FRANKFURT TO VIENNA
Normal price: $146

Sale price: $50