Narrative:

We arrived in ZZZ and swapped to aircraft XXX. This aircraft had two mels; one was the number two engine anti ice cowl valve failed in the open position. The other was the number one engine bleed air shut-off valve (prsov) was closed. This MEL was added in ZZZ as the previous crew made a logbook entry for left engine bleed trip. The number two engine anti-ice valve was locked in the open position and high stage valve was locked closed per MEL sp #30 - ice and rain protection. We were dispatched at FL250. During cruise flight we were directed by ATC to slow to 260 knots. As the throttles moved towards idle; the cabin altitude began to climb at 3000 fpm. I pushed the power up and regained control of the cabin altitude. During descent into ZZZ1; I maintained approximately 1000 fpm descent rate. This maintained control of the cabin altitude. The APU was started and at 17;000 ft; we powered the left pack with the APU. The rest of the descent was normal.

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Original NASA ASRS Text

Title: B737-700 flight crew reported 2 MELs that when combined did not provide sufficient bleed air to properly pressurize the aircraft during descent.

Narrative: We arrived in ZZZ and swapped to aircraft XXX. This aircraft had two MELs; one was the number two engine anti ice cowl valve failed in the open position. The other was the number one engine bleed air shut-off valve (PRSOV) was closed. This MEL was added in ZZZ as the previous crew made a logbook entry for left engine bleed trip. The number two engine anti-ice valve was locked in the open position and high stage valve was locked closed per MEL SP #30 - Ice and Rain Protection. We were dispatched at FL250. During cruise flight we were directed by ATC to slow to 260 knots. As the throttles moved towards idle; the cabin altitude began to climb at 3000 fpm. I pushed the power up and regained control of the cabin altitude. During descent into ZZZ1; I maintained approximately 1000 fpm descent rate. This maintained control of the cabin altitude. The APU was started and at 17;000 FT; we powered the left pack with the APU. The rest of the descent was normal.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.