Frequently these convoys had as escorts vessels of the British Royal Navy, though generally not past India, or before on the return leg.

For her first six voyages her principal managing owner was Richard Lewin, who was a former commander for the EIC and a member of the United Company of merchants of England trading to the East-Indies.

On the return leg she crossed Second Bar on 15 February, reaching St Helena on 18 June and the Downs on 7 September.

[2] She had sailed with a convoy of Indiamen that were bringing General Alured Clarke and his troops for the invasion of the Cape Colony.

[2] Captain Lestock Wilson left Portsmouth on 17 February 1798 and arrived back on 1 August 1799, having reached Bombay and China.

[2] For her fourth voyage, Exeter was under the command of Captain Henry Meriton, and sailing under a letter of marque issued 24 March 1800.

She was in a convoy with a number of other vessels, particularly the East Indiamen Bombay Castle, Coutts, and Neptune, and under the escort of the 64-gun ship of the line Belliqueux.

On 4 August the convoy was near the island of Trindade off the Brazilian coast, from where they would catch the westerly trade winds that would carry them to Cape of Good Hope.

When the British formed a line of battle, Landolphe thought from the distance that they were a fleet of powerful warships and turned to escape.

[Note 1] Believing himself outgunned, Captain Jean-Daniel Coudin surrendered Médée, only to discover when he came aboard Exeter that she was a merchant vessel.

[2] The captured frigates reached England towards the end of the French Revolutionary Wars and the Royal Navy did not take Concorde into service.

The Royal Navy did purchase Médée, which became HMS Medee, but she was never commissioned and instead served as a prison hulk from 1802 until she was sold in 1805.

Belliqueux, Exeter, Bombay Castle, Coutts, Dorsetshire, and Neptune shared in the prize money for Concorde and Médée.

The Treaty of Amiens collapsed and the Napoleonic Wars broke out after she had left the Downs on 6 April 1803 so her letter of marque was dated 20 June.

[2] On 7 August 1805, HMS Blenheim, Captain Austin Bissell and Rear-Admiral Thomas Troubridge, was escorting a fleet of East Indiamen consisting of Castle Eden, Cumberland, Devonshire, Dorsetshire, Exeter, Hope, and Preston.

For the return trip she crossed Second Bar on 3 February 1806, reached Malacca on 17 March, St Helena on 7 July, and the Downs on 3 September.

For the return voyage she passed the Point de Galle on 25 February 1811, reaching St Helena on 28 May, and anchoring in the Downs on 9 August.