PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 13
Situational Awareness
ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance
Human Factors
Aircraft X was a pilot in training and doing multiple practice approaches to a few of our airports in our airspace. At the time of the incident; he was doing a missed approach off of the DMN airport. On the departure; I had him ident and radar identified him and gave him a turn towards EWM that was a fix down the road on is flight plan. His initial filing was to go missed at DMN; then back to the DMN VOR and join V94 to EWM. Without giving it much thought; I just gave him EWM in a climb to 090. Well; the MIA in that area is 095. I tried to climb him; but realized his rate of climb wasn't going to cut it and then I turned him north to get him out of that area sooner. I should've been more aware of the airspace MIA before turning him early off of his flight plan.  I will be more aware in the future of the MIA on an aircraft doing a missed approach. I don't believe I have any other recommendations.
ZAB ARTCC Controller reported issuing an altitude below the Minimum IFR Altitude to an aircraft; realizing the mistake later reporter turned aircraft before entering the higher MIA.