diff --git a/src/Reporter.cc b/src/Reporter.cc
index a40ddb9a3d..d44eff556b 100644
--- a/src/Reporter.cc
+++ b/src/Reporter.cc
@@ -491,7 +491,7 @@ void Reporter::DoLog(const char* prefix, EventHandlerPtr event, FILE* out,
 		val_list vl(vl_size);
 
 		if ( time )
-			vl.append(new Val((bro_start_network_time != 0.0) ? network_time : 0, TYPE_TIME));
+			vl.append(new Val(network_time ? network_time : current_time(), TYPE_TIME));
 
 		vl.append(new StringVal(buffer));
 
diff --git a/src/broker/Manager.cc b/src/broker/Manager.cc
index e4ef3d570c..1f132ac7cc 100644
--- a/src/broker/Manager.cc
+++ b/src/broker/Manager.cc
@@ -941,6 +941,12 @@ void Manager::Process()
 
 	if ( had_input )
 		{
+		if ( network_time == 0 )
+			// If we're getting Broker messages, but still haven't initialized
+			// network_time, may as well do so now because otherwise the
+			// broker/cluster logs will end up using timestamp 0.
+			net_update_time(current_time());
+
 		++times_processed_without_idle;
 
 		// The max number of Process calls allowed to happen in a row without
diff --git a/testing/btest/Baseline/core.reporter/logger-test.log b/testing/btest/Baseline/core.reporter/logger-test.log
index 1dc58b65cd..0297fbe208 100644
--- a/testing/btest/Baseline/core.reporter/logger-test.log
+++ b/testing/btest/Baseline/core.reporter/logger-test.log
@@ -1,6 +1,6 @@
-reporter_info|init test-info|/Users/jsiwek/Projects/bro/bro/testing/btest/.tmp/core.reporter/reporter.zeek, line 8|0.000000
-reporter_warning|init test-warning|/Users/jsiwek/Projects/bro/bro/testing/btest/.tmp/core.reporter/reporter.zeek, line 9|0.000000
-reporter_error|init test-error|/Users/jsiwek/Projects/bro/bro/testing/btest/.tmp/core.reporter/reporter.zeek, line 10|0.000000
-reporter_info|done test-info|/Users/jsiwek/Projects/bro/bro/testing/btest/.tmp/core.reporter/reporter.zeek, line 15|0.000000
-reporter_warning|done test-warning|/Users/jsiwek/Projects/bro/bro/testing/btest/.tmp/core.reporter/reporter.zeek, line 16|0.000000
-reporter_error|done test-error|/Users/jsiwek/Projects/bro/bro/testing/btest/.tmp/core.reporter/reporter.zeek, line 17|0.000000
+reporter_info|init test-info|/home/jon/pro/zeek/zeek/testing/btest/.tmp/core.reporter/reporter.zeek, line 8|1561700937.882616
+reporter_warning|init test-warning|/home/jon/pro/zeek/zeek/testing/btest/.tmp/core.reporter/reporter.zeek, line 9|1561700937.882616
+reporter_error|init test-error|/home/jon/pro/zeek/zeek/testing/btest/.tmp/core.reporter/reporter.zeek, line 10|1561700937.882616
+reporter_info|done test-info|/home/jon/pro/zeek/zeek/testing/btest/.tmp/core.reporter/reporter.zeek, line 15|1561700937.882616
+reporter_warning|done test-warning|/home/jon/pro/zeek/zeek/testing/btest/.tmp/core.reporter/reporter.zeek, line 16|1561700937.882616
+reporter_error|done test-error|/home/jon/pro/zeek/zeek/testing/btest/.tmp/core.reporter/reporter.zeek, line 17|1561700937.882616
diff --git a/testing/btest/core/reporter.zeek b/testing/btest/core/reporter.zeek
index 8591096c2b..a00cd241ab 100644
--- a/testing/btest/core/reporter.zeek
+++ b/testing/btest/core/reporter.zeek
@@ -1,7 +1,7 @@
 #
-# @TEST-EXEC: zeek %INPUT >output 2>&1
+# @TEST-EXEC: zeek -b %INPUT >output 2>&1
 # @TEST-EXEC: TEST_DIFF_CANONIFIER=$SCRIPTS/diff-remove-abspath btest-diff output
-# @TEST-EXEC: TEST_DIFF_CANONIFIER=$SCRIPTS/diff-remove-abspath btest-diff logger-test.log
+# @TEST-EXEC: TEST_DIFF_CANONIFIER="$SCRIPTS/diff-remove-abspath | $SCRIPTS/diff-remove-timestamps" btest-diff logger-test.log
 
 event zeek_init()
 {