When it became clear that the Aurelia B24 spider wasn't the export success that was hoped for Lancia stopped the production of this model at the end of 1955. Coachbuilder Pininfarina was set to work to create a redesigned version which was less extreme and more practical. This new version appeared in 1956 and was named Aurelia B24 convertible instead of spider (traditionally a small open two-seater with a removable cloth top named after a classic Italian style of carriage with the same features), as to indicate its more sensible nature. To stress its intentions the title "America" was added to the model name. Underneath it was based on the Series 5 chassis of the Aurelia, which was less powerful but more comfortable than the Series 4 chassis of the spider.

Though the convertible looked quite like the preceding spider its body was completely revised and hardly any panels could be exchanged between the two models. It was slightly larger than the spider at 423 x 155 x 130 cm (length x width x height). Most notable differences were the absence of the panoramic wrap-around windshield, the simple one-piece front bumper and the larger doors which were cut out deeper into the sill. The doors now had roll down windows, opening front quarter lights and regular door handles.
These external changes influenced the look and appeal of the car. It appeared more sedate and conservative and probably more in tune with the general taste at the time. Still it remained an elegant sportscar with an unmistakable Italian style.
The spider had been criticized a lot for its awkward driving position so this was corrected in the interior of the convertible. The flat bench-like seats of the spider were replaced by more comfortable separate seats (divided by a padded panel) and ultimately by bucket seats in the convertible. This made the convertible a more relaxed car to drive.
Another problem of the spider was its price. Due to the relatively old-fashioned manner of production the convertible was not much more affordable, though it was a bit cheaper than the spider. Instead of aiming at youthful American car buyers with a limited budget the convertible was redirected to please affluent customers looking for a quality car.

Production of the convertible followed that of the GT which meant that in 1957 the convertible received the Series 6 modifications. In Series 5 form the 2,5-litre V6 Aurelia engine produced 110 hp @ 5000 rpm and pushed the 1215 kg heavy convertible to a maximum speed of 172 kph. The Series 6 version of this engine produced 112 hp @ 5000 rpm and was a bit more lively than the Series 5. The new gearbox and clutch, larger brakes and improved suspension of the Series 5 and 6 chassis added to the increased comfort and ease to drive of the convertible compared to the more performance oriented and temperamental spider.
In 1958 the manufacture of the convertible was stopped, together with that of the GT. During this production run there were very little changes to the outside of the car. Most visible differences between the S5 (1956) and S6 (1957-1958) convertible were the modern, separate bucket seats of the S6 (see the top picture on this page) and the addition of overriders on the bumpers. Another, much less visible, distinguishing feature was the fuel tank: in the last 220 convertibles it was placed in the trunk instead of behind the seats. In total 519 convertibles were made, 149 of the S5 and 370 of the S6 version. All were left hand drive.

Being less rare and exuberant than the spider the value and appreciation of the convertible is to some extent overshadowed by that of the spider. But as it is more practical and better to drive there are plenty of enthusiasts for this model. As a result cars like these are not often on the market and certainly not at a bargain. Mechanical parts for the Aurelia B24 convertible these days are readily available but restoring the body can be arduous and expensive. But as it is considered to be one of the prettiest and practical Italian open two-seaters it may be worth it.