IMac randomly wakes up from sleep

My iMac (27-inch, Late 2012) randomly wakes up, up to 9 times a day. I'm using El Capitan 10.11.3 (15D21).

A syslog | grep -i "Wake reason" shows the following many times:

Apr  5 00:02:50 Nikolajs-iMac kernel[0] <Notice>: Wake reason: EC.SleepTimer (SleepTimer)
Apr  5 00:02:52 Nikolajs-iMac kernel[0] <Notice>: [HID] [ATC] AppleDeviceManagementHIDEventService::processWakeReason Wake reason: Host (0x01)
Apr  6 18:55:24 Nikolajs-iMac kernel[0] <Notice>: Wake reason: EC.PME (User)
Apr  6 18:55:28 Nikolajs-iMac kernel[0] <Notice>: [HID] [ATC] AppleDeviceManagementHIDEventService::processWakeReason Wake reason: Host (0x01)
Apr  6 20:37:16 Nikolajs-iMac kernel[0] <Notice>: Wake reason: EC.SleepTimer (SleepTimer)
Apr  6 20:37:19 Nikolajs-iMac kernel[0] <Notice>: [HID] [ATC] AppleDeviceManagementHIDEventService::processWakeReason Wake reason: Host (0x01)
Apr  6 21:20:03 Nikolajs-iMac kernel[0] <Notice>: Wake reason: EHC1
Apr  6 21:20:04 Nikolajs-iMac kernel[0] <Notice>: [HID] [ATC] AppleDeviceManagementHIDEventService::processWakeReason Wake reason: Button (0x03)
Apr  6 22:31:19 Nikolajs-iMac kernel[0] <Notice>: Wake reason: EC.SleepTimer (SleepTimer)
Apr  6 22:31:21 Nikolajs-iMac kernel[0] <Notice>: [HID] [ATC] AppleDeviceManagementHIDEventService::processWakeReason Wake reason: Host (0x01)

There aren't any usb devices connected, nor any bluetooth devices, except the keyboard and mouse.

The most obvious reasons, power nap and wake on lan, aren't turned on. I've already tried to toggle them but it didn't help. What else could this be?

I've googled for answers for a long time, many times, already, but I couldn't find any solution to this. The problem already persists for at least two major OSX versions.

Thanks a lot!

Update:

➜  ~ pmset -g assertions
2016-04-12 18:30:18 +0200
Assertion status system-wide:
   BackgroundTask                 0
   ApplePushServiceTask           0
   UserIsActive                   1
   PreventUserIdleDisplaySleep    0
   PreventSystemSleep             0
   ExternalMedia                  0
   PreventUserIdleSystemSleep     1
   NetworkClientActive            0
Listed by owning process:
   pid 526(storedownloadd): [0x000049be000112c7] 143:31:30 PreventUserIdleSystemSleep named: "URLConnection in progress"
   pid 100(hidd): [0x0000bf4b00091335] 00:18:20 UserIsActive named: "com.apple.iohideventsystem.queue.tickle"
    Timeout will fire in 219 secs Action=TimeoutActionRelease
Kernel Assertions: 0x8=BT-HID
   id=501  level=255 0x8=BT-HID mod=01.01.70, 01:00 description=com.apple.driver.IOBluetoothHIDDriver owner=AppleHSBluetoothDevice
   id=502  level=255 0x8=BT-HID mod=01.01.70, 01:00 description=com.apple.driver.IOBluetoothHIDDriver owner=AppleBluetoothHIDKeyboard
Idle sleep preventers: IODisplayWrangler

Update 2: I managed to enter the pmset -g assertions right after the imac woke up last night. Here is the output:

➜  ~ pmset -g assertions
2016-04-16 22:40:16 +0200
Assertion status system-wide:
   BackgroundTask                 1
   ApplePushServiceTask           0
   UserIsActive                   0
   PreventUserIdleDisplaySleep    0
   InteractivePushServiceTask     1
   PreventSystemSleep             0
   ExternalMedia                  0
   PreventUserIdleSystemSleep     1
   NetworkClientActive            0
   InternalPreventSleep           1
Listed by owning process:
   pid 62023(AddressBookSourceSync): [0x000159c300010639] 00:00:06 PreventUserIdleSystemSleep named: "Address Book Source Sync"
    Timeout will fire in 1794 secs Action=TimeoutActionTurnOff
   pid 204(backupd-helper): [0x000159c3000b062b] 00:00:06 BackgroundTask named: "backupd-helper"
   pid 186(coreaudiod): [0x000159c8000101e8] 00:00:00 PreventUserIdleSystemSleep named: "com.apple.audio.AppleHDAEngineOutput:1B,0,1,2:0.context.preventuseridlesleep"
    Created for PID: 249.
   pid 62024(AddressBookSourceSync): [0x000159c30001063b] 00:00:06 PreventUserIdleSystemSleep named: "Address Book Source Sync"
    Timeout will fire in 1794 secs Action=TimeoutActionTurnOff
   pid 625(UserEventAgent): [0x000159c3000b063a] 00:00:06 BackgroundTask named: "com.apple.AddressBook.ScheduledSync"
    Created for PID: 62023.
   pid 526(storedownloadd): [0x000049be000112c7] 243:41:28 PreventUserIdleSystemSleep named: "URLConnection in progress"
   pid 62025(softwareupdate_notify_agent): [0x000159c3000b063d] 00:00:05 BackgroundTask named: "com.apple.softwareupdate.NotifyAgentAssertion"
   pid 79(apsd): [0x000159c80012064e] 00:00:01 InteractivePushServiceTask named: "com.apple.apsd-lastpowerassertionlinger"
    Timeout will fire in 86399 secs Action=TimeoutActionTurnOff
   pid 56(powerd): [0x000159b9000d061b] 00:00:16 InternalPreventSleep named: "com.apple.powermanagement.acwakelinger"
    Timeout will fire in 29 secs Action=TimeoutActionRelease
Kernel Assertions: 0x8=BT-HID
   id=501  level=255 0x8=BT-HID mod=01.01.70, 01:00 description=com.apple.driver.IOBluetoothHIDDriver owner=AppleHSBluetoothDevice
   id=502  level=255 0x8=BT-HID mod=01.01.70, 01:00 description=com.apple.driver.IOBluetoothHIDDriver owner=AppleBluetoothHIDKeyboard
Idle sleep preventers: IODisplayWrangler