We measure the absorption of thin InGaAs/InP quantum wells with a well width between 0 and 20 A˚. The discretization of the transition energies due to the quantization of the well width by monolayers is clearly observed for both the heavy and light hole excitons. The dependences of the heavy and light hole transition energies on the InGaAs growth time are investigated and show striking differences. This is discussed in relation to the atomic steps at the interfaces of the wells. The measured heavy and light hole transition energies agree well with calculation, which takes the split‐off holes into account.