[G2 and Desire Z Q&A, Help & Troubleshooting] dartbider:
Here are the results. Note that From the moment I turned the screen off at around 3:11, the screen woke up around 3 times. Twice at 3:19, and once at 3:20.

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-------- beginning of /dev/log/system

08-31 03:10:58.473 1291 1749 W InputManagerService: Window already focused, ignoring focus gain of: com.android.internal.view.IInputMethodClient$Stub$Proxy@40962720

--------- beginning of /dev/log/main

08-31 03:11:00.685 1291 1328 I power : *** set_screen_state 0

08-31 03:11:00.685 1291 1328 D SensorService: disable: connection.get() = 0x3eb008

08-31 03:11:00.685 1291 1328 D SensorService: disable: get sensor name = CM3602 Light sensor

08-31 03:11:00.695 1291 1328 D SensorService: pid=1291, uid=1000

08-31 03:11:00.695 1291 1328 D SensorService: Active sensors:

08-31 03:11:00.695 1291 1328 D SensorService: BMA150 3-axis Accelerometer (handle=0x00000000, connections=1)

08-31 03:11:00.695 1291 1328 D lights : set_light_keyboard brightness=0

08-31 03:11:00.695 1291 1323 D SensorService: disable: connection.get() = 0x3eb008

08-31 03:11:00.695 1291 1323 D SensorService: disable: get sensor name = BMA150 3-axis Accelerometer

08-31 03:11:00.695 1291 1323 D Sensors : Enable akm: en = 0

08-31 03:11:00.695 1291 1323 D SensorService: pid=1291, uid=1000

08-31 03:11:00.695 1291 1323 D SensorService: Active sensors:

08-31 03:11:00.695 1291 1326 D KeyguardViewManager: show(); mKeyguardView==null

08-31 03:11:00.695 1291 1326 D KeyguardViewManager: keyguard view is null, creating it...

08-31 03:11:00.765 4367 4367 W IInputConnectionWrapper: getExtractedText on inactive InputConnection

08-31 03:11:00.765 4367 4367 W IInputConnectionWrapper: getExtractedText on inactive InputConnection

08-31 03:11:00.845 1404 1404 D Database: dbopen(): path = /data/data/com.google.android.gsf/databases/gls.db, flag = 6, file size = 5120

08-31 03:11:00.845 1404 1404 D Database: dbopen(): path = /data/data/com.google.android.gsf/databases/gls.db, journal mode: wal, storage free size = 885 M

08-31 03:11:00.875 4367 4367 W IInputConnectionWrapper: getExtractedText on inactive InputConnection

08-31 03:11:00.875 4367 4367 W IInputConnectionWrapper: getExtractedText on inactive InputConnection

08-31 03:11:00.885 1291 1299 D SurfaceFlinger: About to give-up screen, flinger = 0x23eb60

08-31 03:11:00.965 1780 1780 D dalvikvm: GC_EXPLICIT freed 294K, 51% free 2998K/6087K, external 1625K/2137K, paused 138ms

08-31 03:11:01.035 1780 1780 D dalvikvm: GC_EXPLICIT freed 303K, 51% free 3003K/6087K, external 1625K/2137K, paused 30ms

08-31 03:11:01.196 1225 1225 D AK8975 : Compass CLOSE

08-31 03:15:38.260 1291 1749 D dalvikvm: GC_EXPLICIT freed 1129K, 38% free 6978K/11143K, external 5168K/5467K, paused 131ms

08-31 03:19:33.610 1780 1780 D dalvikvm: GC_EXPLICIT freed 311K, 51% free 3002K/6087K, external 1625K/2137K, paused 39ms

08-31 03:19:44.930 1291 1291 I power : *** set_screen_state 1

08-31 03:19:44.940 1291 1291 D SensorService: enable: connection.get() = 0x3eb008

08-31 03:19:44.940 1291 1291 D SensorService: enable: get sensor name = CM3602 Light sensor

08-31 03:19:44.940 1291 1291 D SensorService: pid=1291, uid=1000

08-31 03:19:44.940 1291 1291 D SensorService: Active sensors:

08-31 03:19:44.940 1291 1291 D SensorService: CM3602 Light sensor (handle=0x00000004, connections=1)

08-31 03:19:44.950 1291 1323 D PowerManagerService: bl_tmp:80

08-31 03:19:44.950 1291 1323 D PowerManagerService: New lightsensor value:10, lcdValue:160

08-31 03:19:44.950 1291 1323 D PowerManagerService: lightSensorChangedLocked, buttonValue >= 0, mPowerState = 3

08-31 03:19:44.950 1291 1323 D lights : set_light_keyboard brightness=0

08-31 03:19:44.950 1291 1326 D KeyguardViewManager: onScreenTurnedOn()

08-31 03:19:44.960 1291 1323 D SensorService: enable: connection.get() = 0x3eb008

08-31 03:19:44.960 1291 1323 D SensorService: enable: get sensor name = BMA150 3-axis Accelerometer

08-31 03:19:44.960 1291 1323 D Sensors : Enable akm: en = 1

08-31 03:19:44.990 1291 1323 D SensorService: pid=1291, uid=1000

08-31 03:19:44.990 1291 1323 D SensorService: Active sensors:

08-31 03:19:44.990 1291 1323 D SensorService: BMA150 3-axis Accelerometer (handle=0x00000000, connections=1)

08-31 03:19:44.990 1291 1323 D SensorService: CM3602 Light sensor (handle=0x00000004, connections=1)

08-31 03:19:45.000 1225 1225 D AK8975 : Compass Start

08-31 03:19:45.020 1291 1299 D SurfaceFlinger: Screen about to return, flinger = 0x23eb60

08-31 03:19:50.045 1291 1417 I power : *** set_screen_state 0

08-31 03:19:50.045 1291 1417 D SensorService: disable: connection.get() = 0x3eb008

08-31 03:19:50.045 1291 1417 D SensorService: disable: get sensor name = CM3602 Light sensor

08-31 03:19:50.045 1291 1417 D SensorService: pid=1291, uid=1000

08-31 03:19:50.045 1291 1417 D SensorService: Active sensors:

08-31 03:19:50.045 1291 1417 D SensorService: BMA150 3-axis Accelerometer (handle=0x00000000, connections=1)

08-31 03:19:50.045 1291 1417 D lights : set_light_keyboard brightness=0

08-31 03:19:50.055 1291 1323 D SensorService: disable: connection.get() = 0x3eb008

08-31 03:19:50.055 1291 1323 D SensorService: disable: get sensor name = BMA150 3-axis Accelerometer

08-31 03:19:50.055 1291 1323 D Sensors : Enable akm: en = 0

08-31 03:19:50.055 1291 1323 D SensorService: pid=1291, uid=1000

08-31 03:19:50.055 1291 1323 D SensorService: Active sensors:

08-31 03:19:50.055 1291 1326 D KeyguardViewManager: onScreenTurnedOff()

08-31 03:19:50.055 1291 1326 D KeyguardViewManager: reset()

08-31 03:19:50.125 4367 4367 W IInputConnectionWrapper: getExtractedText on inactive InputConnection

08-31 03:19:50.125 4367 4367 W IInputConnectionWrapper: getExtractedText on inactive InputConnection

08-31 03:19:50.205 1780 1780 D dalvikvm: GC_EXPLICIT freed 314K, 51% free 3000K/6087K, external 1625K/2137K, paused 33ms

08-31 03:19:50.225 1291 1299 D SurfaceFlinger: About to give-up screen, flinger = 0x23eb60

08-31 03:19:50.275 1780 1780 D dalvikvm: GC_EXPLICIT freed 306K, 51% free 3001K/6087K, external 1625K/2137K, paused 31ms

08-31 03:19:50.536 1225 1225 D AK8975 : Compass CLOSE

08-31 03:19:59.520 1291 1365 D SntpClient: request time failed: java.net.UnknownHostException: north-america.pool.ntp.org

08-31 03:19:59.560 1291 1365 D SntpClient: request time failed: java.net.UnknownHostException: north-america.pool.ntp.org

08-31 03:19:59.560 1291 1365 D SntpClient: request time failed: java.net.UnknownHostException: north-america.pool.ntp.org

08-31 03:19:59.960 1291 1296 I power : *** set_screen_state 1

08-31 03:19:59.970 1291 1296 D SensorService: enable: connection.get() = 0x3eb008

08-31 03:19:59.970 1291 1296 D SensorService: enable: get sensor name = CM3602 Light sensor

08-31 03:19:59.970 1291 1296 D SensorService: pid=1291, uid=1000

08-31 03:19:59.970 1291 1296 D SensorService: Active sensors:

08-31 03:19:59.970 1291 1296 D SensorService: CM3602 Light sensor (handle=0x00000004, connections=1)

08-31 03:19:59.980 1291 1323 D PowerManagerService: bl_tmp:80

08-31 03:19:59.980 1291 1323 D PowerManagerService: New lightsensor value:10, lcdValue:160

08-31 03:19:59.980 1291 1323 D PowerManagerService: lightSensorChangedLocked, buttonValue >= 0, mPowerState = 3

08-31 03:19:59.980 1291 1323 D lights : set_light_keyboard brightness=0

08-31 03:19:59.980 1291 1326 D KeyguardViewManager: onScreenTurnedOn()

08-31 03:19:59.990 1291 1323 D SensorService: enable: connection.get() = 0x3eb008

08-31 03:19:59.990 1291 1323 D SensorService: enable: get sensor name = BMA150 3-axis Accelerometer

08-31 03:19:59.990 1291 1323 D Sensors : Enable akm: en = 1

08-31 03:20:00.000 1291 1323 D SensorService: pid=1291, uid=1000

08-31 03:20:00.000 1291 1323 D SensorService: Active sensors:

08-31 03:20:00.000 1291 1323 D SensorService: BMA150 3-axis Accelerometer (handle=0x00000000, connections=1)

08-31 03:20:00.000 1291 1323 D SensorService: CM3602 Light sensor (handle=0x00000004, connections=1)

08-31 03:20:00.020 1225 1225 D AK8975 : Compass Start

08-31 03:20:00.050 1291 1299 D SurfaceFlinger: Screen about to return, flinger = 0x23eb60

08-31 03:20:05.014 1291 1401 I power : *** set_screen_state 0

08-31 03:20:05.014 1291 1401 D SensorService: disable: connection.get() = 0x3eb008

08-31 03:20:05.014 1291 1401 D SensorService: disable: get sensor name = CM3602 Light sensor

08-31 03:20:05.034 1291 1401 D SensorService: pid=1291, uid=1000

08-31 03:20:05.034 1291 1401 D SensorService: Active sensors:

08-31 03:20:05.034 1291 1401 D SensorService: BMA150 3-axis Accelerometer (handle=0x00000000, connections=1)

08-31 03:20:05.034 1291 1401 D lights : set_light_keyboard brightness=0

08-31 03:20:05.044 1291 1323 D SensorService: disable: connection.get() = 0x3eb008

08-31 03:20:05.044 1291 1323 D SensorService: disable: get sensor name = BMA150 3-axis Accelerometer

08-31 03:20:05.044 1291 1323 D Sensors : Enable akm: en = 0

08-31 03:20:05.044 1291 1323 D SensorService: pid=1291, uid=1000

08-31 03:20:05.044 1291 1323 D SensorService: Active sensors:

08-31 03:20:05.044 1291 1326 D KeyguardViewManager: onScreenTurnedOff()

08-31 03:20:05.044 1291 1326 D KeyguardViewManager: reset()

08-31 03:20:05.204 1291 1299 D SurfaceFlinger: About to give-up screen, flinger = 0x23eb60

08-31 03:20:05.224 4367 4367 W IInputConnectionWrapper: getExtractedText on inactive InputConnection

08-31 03:20:05.224 4367 4367 W IInputConnectionWrapper: getExtractedText on inactive InputConnection

08-31 03:20:05.555 1225 1225 D AK8975 : Compass CLOSE

08-31 03:20:15.530 1291 1291 I power : *** set_screen_state 1

08-31 03:20:15.530 1291 1291 D SensorService: enable: connection.get() = 0x3eb008

08-31 03:20:15.530 1291 1291 D SensorService: enable: get sensor name = CM3602 Light sensor

08-31 03:20:15.540 1291 1291 D SensorService: pid=1291, uid=1000

08-31 03:20:15.540 1291 1291 D SensorService: Active sensors:

08-31 03:20:15.540 1291 1291 D SensorService: CM3602 Light sensor (handle=0x00000004, connections=1)

08-31 03:20:15.550 1291 1323 D PowerManagerService: bl_tmp:80

08-31 03:20:15.550 1291 1323 D PowerManagerService: New lightsensor value:10, lcdValue:160

08-31 03:20:15.550 1291 1323 D PowerManagerService: lightSensorChangedLocked, buttonValue >= 0, mPowerState = 3

08-31 03:20:15.550 1291 1323 D lights : set_light_keyboard brightness=0

08-31 03:20:15.550 1291 1326 D KeyguardViewManager: onScreenTurnedOn()

08-31 03:20:15.570 1291 1323 D SensorService: enable: connection.get() = 0x3eb008

08-31 03:20:15.570 1291 1323 D SensorService: enable: get sensor name = BMA150 3-axis Accelerometer

08-31 03:20:15.570 1291 1323 D Sensors : Enable akm: en = 1

08-31 03:20:15.570 1291 1323 D SensorService: pid=1291, uid=1000

08-31 03:20:15.570 1291 1323 D SensorService: Active sensors:

08-31 03:20:15.570 1291 1323 D SensorService: BMA150 3-axis Accelerometer (handle=0x00000000, connections=1)

08-31 03:20:15.570 1291 1323 D SensorService: CM3602 Light sensor (handle=0x00000004, connections=1)

08-31 03:20:15.680 1291 1299 D SurfaceFlinger: Screen about to return, flinger = 0x23eb60

08-31 03:20:15.780 1225 1225 D AK8975 : Compass Start

08-31 03:20:20.734 1291 1752 I power : *** set_screen_state 0

08-31 03:20:20.734 1291 1752 D SensorService: disable: connection.get() = 0x3eb008

08-31 03:20:20.734 1291 1752 D SensorService: disable: get sensor name = CM3602 Light sensor

08-31 03:20:20.734 1291 1752 D SensorService: pid=1291, uid=1000

08-31 03:20:20.734 1291 1752 D SensorService: Active sensors:

08-31 03:20:20.734 1291 1752 D SensorService: BMA150 3-axis Accelerometer (handle=0x00000000, connections=1)

08-31 03:20:20.734 1291 1752 D lights : set_light_keyboard brightness=0

08-31 03:20:20.734 1291 1323 D SensorService: disable: connection.get() = 0x3eb008

08-31 03:20:20.734 1291 1323 D SensorService: disable: get sensor name = BMA150 3-axis Accelerometer

08-31 03:20:20.734 1291 1323 D Sensors : Enable akm: en = 0

08-31 03:20:20.734 1291 1323 D SensorService: pid=1291, uid=1000

08-31 03:20:20.734 1291 1323 D SensorService: Active sensors:

08-31 03:20:20.734 1291 1326 D KeyguardViewManager: onScreenTurnedOff()

08-31 03:20:20.734 1291 1326 D KeyguardViewManager: reset()

08-31 03:20:20.804 4367 4367 W IInputConnectionWrapper: getExtractedText on inactive InputConnection

08-31 03:20:20.804 4367 4367 W IInputConnectionWrapper: getExtractedText on inactive InputConnection

08-31 03:20:20.904 1291 1299 D SurfaceFlinger: About to give-up screen, flinger = 0x23eb60

08-31 03:20:20.944 1225 1225 D AK8975 : Compass CLOSE

08-31 03:20:21.430 1291 1328 D KeyguardViewMediator: wakeWhenReadyLocked(26)

08-31 03:20:21.430 1291 1326 D KeyguardViewManager: wakeWhenReady(26)

08-31 03:20:21.440 1291 1326 I power : *** set_screen_state 1

08-31 03:20:21.440 1291 1326 D SensorService: enable: connection.get() = 0x3eb008

08-31 03:20:21.440 1291 1326 D SensorService: enable: get sensor name = CM3602 Light sensor

08-31 03:20:21.440 1291 1326 D SensorService: pid=1291, uid=1000

08-31 03:20:21.440 1291 1326 D SensorService: Active sensors:

08-31 03:20:21.440 1291 1326 D SensorService: CM3602 Light sensor (handle=0x00000004, connections=1)

08-31 03:20:21.440 1291 1323 D SensorService: enable: connection.get() = 0x3eb008

08-31 03:20:21.440 1291 1323 D SensorService: enable: get sensor name = BMA150 3-axis Accelerometer

08-31 03:20:21.440 1291 1323 D Sensors : Enable akm: en = 1

08-31 03:20:21.440 1291 1323 D SensorService: pid=1291, uid=1000

08-31 03:20:21.440 1291 1323 D SensorService: Active sensors:

08-31 03:20:21.440 1291 1323 D SensorService: BMA150 3-axis Accelerometer (handle=0x00000000, connections=1)

08-31 03:20:21.440 1291 1323 D SensorService: CM3602 Light sensor (handle=0x00000004, connections=1)

08-31 03:20:21.440 1291 1326 D KeyguardViewManager: onScreenTurnedOn()

08-31 03:20:21.520 1291 1323 D PowerManagerService: bl_tmp:80

08-31 03:20:21.530 1291 1323 D PowerManagerService: New lightsensor value:10, lcdValue:160

08-31 03:20:21.530 1291 1323 D PowerManagerService: lightSensorChangedLocked, buttonValue >= 0, mPowerState = 3

08-31 03:20:21.540 1291 1323 D lights : set_light_keyboard brightness=0

08-31 03:20:21.560 1291 1299 D SurfaceFlinger: Screen about to return, flinger = 0x23eb60

08-31 03:20:21.670 1225 1225 D AK8975 : Compass Start

08-31 03:20:22.701 1291 1326 D KeyguardViewManager: hide()

08-31 03:20:22.751 1291 1754 W InputManagerService: Window already focused, ignoring focus gain of: com.android.internal.view.IInputMethodClient$Stub$Proxy@409d70e0

08-31 03:20:23.201 1291 1326 D KeyguardViewManager: hide(); digitalClock OOM removeViewFromWindow

08-31 03:20:26.184 1291 1750 W InputManagerService: Window already focused, ignoring focus gain of: com.android.internal.view.IInputMethodClient$Stub$Proxy@409deea0