Swiss Air is as bad as Ryan Air! Trying to rip you off any chance they get! I bought their ticket online completely oblivious to the fact that I'm not allowed luggage (because it was a third party site), it did not mention the fact I'm not allowed luggage. I travelled with a baby and baby wasn't entitled any bag either (although their website claims babies are entitled 1 bag regardless of travel class).
I only found out when I rang them to check my luggage allowance. They said both baby and I are not allowed any luggage! So I asked them to buy an additional bag and gave them my card details to purchase it. However they never mentioned it was only one way! When I was checking in for my return flight I was charged another 30 euros to return the bag back! They conveniently forgot to mention that I was paying only one way (you would think they would at least mention it) and slapped me with a massive fee on the way back. Also beware if you are buying a Swiss Air ticket via web or a third party, they never mention the fact that you're not allowed any luggage.
Also their staff forgot to check me in for my connecting flight which was a nightmare because I didn't know which gates to go to and their transfer desk at Zurich Airport was empty. They also forgot to link the baby to my flight so I had a lot of problems checking in. However they didn't forget to charge me the additional fee for the one and only bag I made the trip with!