diff --git a/third_party/mach_override/mach_override.c b/third_party/mach_override/mach_override.c
index 85a75e5c2067..ca68c0e90e61 100644
--- a/third_party/mach_override/mach_override.c
+++ b/third_party/mach_override/mach_override.c
@@ -8,6 +8,7 @@
 #include "udis86.h"
 #endif
 
+#include <libkern/OSAtomic.h>
 #include <mach-o/dyld.h>
 #include <mach/mach_init.h>
 #include <mach/vm_map.h>
@@ -41,7 +42,7 @@ long kIslandTemplate[] = {
 #define kInstructionHi		10
 #define kInstructionLo		11
 
-#elif defined(__i386__) 
+#elif defined(__i386__)
 
 #define kOriginalInstructionsSize 16
 
@@ -61,6 +62,7 @@ char kIslandTemplate[] = {
 #define kOriginalInstructionsSize 32
 
 #define kJumpAddress    kOriginalInstructionsSize + 6
+#define kMaxJumpOffset  (0x7fffffffUL)
 
 char kIslandTemplate[] = {
 	// kOriginalInstructionsSize nop instructions so that we 
@@ -93,6 +95,14 @@ typedef	struct	{
 	int		allocatedHigh;
 }	BranchIsland;
 
+/**************************
+*
+*	Statistics
+*
+**************************/
+static volatile int64_t __attribute__((__aligned__((sizeof(int64_t)))))
+    g_mach_override_allocation_attempts = 0;
+
 /**************************
 *	
 *	Funky Protos
@@ -101,6 +111,10 @@ typedef	struct	{
 #pragma mark	-
 #pragma mark	(Funky Protos)
 
+u_int64_t mach_override_ptr_allocation_attempts() {
+  return OSAtomicAdd64(0, &g_mach_override_allocation_attempts);
+}
+
 	mach_error_t
 allocateBranchIsland(
 		BranchIsland	**island,
@@ -267,7 +281,13 @@ mach_override_ptr(
 
 #if defined(__i386__) || defined(__x86_64__)
 	if (!err) {
-		uint32_t addressOffset = ((char*)escapeIsland - (char*)originalFunctionPtr - 5);
+		// TODO: On 64-bit, move to opcode FF/4 (jmp 64-bit absolute indirect)
+		// instead of E9 (jmp 32-bit relative to RIP). Then we should update
+		// allocateBranchIsland to simply allocate any page in the address space.
+		// See the 64-bit version of kIslandTemplate array.
+		int64_t addressOffset64 = ((char*)escapeIsland - (char*)originalFunctionPtr - 5);
+		int32_t addressOffset = addressOffset64;
+		assert(addressOffset64 == addressOffset);
 		addressOffset = OSSwapInt32(addressOffset);
 		
 		jumpRelativeInstruction |= 0xE900000000000000LL; 
@@ -385,13 +405,14 @@ allocateBranchIsland(
 		void *originalFunctionAddress)
 {
 	assert( island );
-	
+
 	mach_error_t	err = err_none;
 	
 	if( allocateHigh ) {
 		assert( sizeof( BranchIsland ) <= PAGE_SIZE );
 		vm_address_t page = 0;
 #if defined(__i386__)
+		OSAtomicAdd64(1, &g_mach_override_allocation_attempts);
 		err = vm_allocate( mach_task_self(), &page, PAGE_SIZE, VM_FLAGS_ANYWHERE );
 		if( err == err_none )
 			*island = (BranchIsland*) page;
@@ -401,23 +422,42 @@ allocateBranchIsland(
 		vm_address_t first = 0xfeffffff;
 		vm_address_t last = 0xfe000000 + PAGE_SIZE;
 #elif defined(__x86_64__)
-		// 64-bit ASLR is in bits 13-28
-		vm_address_t first = ((uint64_t)originalFunctionAddress & ~( (0xFUL << 28) | (PAGE_SIZE - 1) ) ) | (0x1UL << 31);
-		vm_address_t last = (uint64_t)originalFunctionAddress & ~((0x1UL << 32) - 1);
+		// This logic is more complex due to the 32-bit limit of the jump out
+		// of the original function. Once that limitation is removed, we can
+		// use vm_allocate with VM_FLAGS_ANYWHERE as in the i386 code above.
+		const uint64_t kPageMask = ~(PAGE_SIZE - 1);
+		vm_address_t first = (uint64_t)originalFunctionAddress - kMaxJumpOffset;
+		first = (first & kPageMask) + PAGE_SIZE; // Align up to the next page start
+		if (first > (uint64_t)originalFunctionAddress) first = 0;
+		vm_address_t last = (uint64_t)originalFunctionAddress + kMaxJumpOffset;
+		if (last < (uint64_t)originalFunctionAddress) last = ULONG_MAX;
 #endif
 
 		page = first;
 		int allocated = 0;
 		vm_map_t task_self = mach_task_self();
 
-		while( !err && !allocated && page != last ) {
+		while( !err && !allocated && page < last ) {
 
+			OSAtomicAdd64(1, &g_mach_override_allocation_attempts);
 			err = vm_allocate( task_self, &page, PAGE_SIZE, 0 );
 			if( err == err_none )
 				allocated = 1;
-			else if( err == KERN_NO_SPACE ) {
+			else if( err == KERN_NO_SPACE || err == KERN_INVALID_ADDRESS) {
 #if defined(__x86_64__)
-				page -= PAGE_SIZE;
+				// This memory region is not suitable, skip it:
+				vm_size_t region_size;
+				mach_msg_type_number_t int_count = VM_REGION_BASIC_INFO_COUNT_64;
+				vm_region_basic_info_data_64_t vm_region_info;
+				mach_port_t object_name;
+				// The call will move 'page' to the beginning of the region:
+				err = vm_region_64(task_self, &page, &region_size,
+							VM_REGION_BASIC_INFO_64, (vm_region_info_t)&vm_region_info,
+							&int_count, &object_name);
+				if (err == KERN_SUCCESS)
+					page += region_size;
+				else
+					break;
 #else
 				page += PAGE_SIZE;
 #endif
@@ -430,6 +470,7 @@ allocateBranchIsland(
 			err = KERN_NO_SPACE;
 #endif
 	} else {
+		OSAtomicAdd64(1, &g_mach_override_allocation_attempts);
 		void *block = malloc( sizeof( BranchIsland ) );
 		if( block )
 			*island = block;
@@ -438,7 +479,7 @@ allocateBranchIsland(
 	}
 	if( !err )
 		(**island).allocatedHigh = allocateHigh;
-	
+
 	return err;
 }
 
diff --git a/third_party/mach_override/mach_override.h b/third_party/mach_override/mach_override.h
index ecd319c1cd7a..253f273d16b6 100644
--- a/third_party/mach_override/mach_override.h
+++ b/third_party/mach_override/mach_override.h
@@ -37,6 +37,18 @@ mach_override_ptr(
     const void *overrideFunctionAddress,
     void **originalFunctionReentryIsland );
 
+/****************************************************************************************
+	mach_override_ptr makes multiple allocation attempts with vm_allocate or malloc,
+  until a suitable address is found for the branch islands. This method returns the
+  global number of such attempts made by all mach_override_ptr calls so far. This
+  statistic is provided for testing purposes and it can be off, if mach_override_ptr
+  is called by multiple threads.
+
+	@result									<-	Total number of vm_allocate calls so far.
+
+	************************************************************************************/
+u_int64_t mach_override_ptr_allocation_attempts();
+
 __END_DECLS
 
 /****************************************************************************************