For those interested in pursuing Panama as a choice for a second passport there is an important clarification.
It is true that on paper Panama does not recognize dual citizenship and requires you to renounce your previous citizenship in order to be naturalized. However, this does not mean you have to really give up your existing citizenship.
The Panamanian nationality law requires an oath of renunciation of former citizenship as a condition of naturalization. However, currently the US court system interprets this oath as "non-meaningful" and therefore it will not result in the loss of US citizenship, unless the US citizen renounces their citizenship directly to the US State Department, which will then result in loss of US nationality.
That said, it is not necessary to renounce US citizenship to the US State Department to become naturalized in Panama.