"I will sleep after I eat."

Translation: Saya akan tidur setelah saya makan.

[phil727975]

Is the second 'saya' really necessary?

[roberta896247]

Saya tidur dulu baru makan

[JerLV]

The present simple of eat slightly disturbs me. Am I too rigid if I want it to be "after I ate" or "after I'll have eaten" ?