odavati

1. (a secret, information) to reveal; to give away; to disclose
   Ona nikad ne odaje tuđe tajne. — She never gives away other people's secrets.
   Novinar ne odaje svoje izvore. — A journalist doesn't reveal his sources.
2. (of feelings, traits) to betray; to show
   Lice mu je odavalo umor. — His face showed his tiredness.
   Njegovo ponašanje odaje ozbiljnost. — His behaviour shows seriousness.
3. (tribute, credit) to pay; to give; to bestow
   Građani svake godine odaju počast žrtvama rata. — Every year citizens pay tribute to the victims of the war.
4. (odavati se + dat.) to indulge in; to take to
   Posle razvoda počeo je da se odaje piću. — After the divorce he took to drink.
5. (heat, light, smell) to emit; to give off
   Peć odaje prijatnu toplotu. — The stove gives off a pleasant heat.

When paying tribute, the recipient is in the dative: odavati počast žrtvama; the perfective is odati.