diff --git a/modules/juce_core/time/juce_Time.cpp b/modules/juce_core/time/juce_Time.cpp
index 882ecfb654..3df84e081c 100644
--- a/modules/juce_core/time/juce_Time.cpp
+++ b/modules/juce_core/time/juce_Time.cpp
@@ -677,7 +677,10 @@ public:
 
         expect (Time (1982, 1, 1, 12, 0, 0, 0, true) + RelativeTime::days (365) == Time (1983, 1, 1, 12, 0, 0, 0, true));
         expect (Time (1970, 1, 1, 12, 0, 0, 0, true) + RelativeTime::days (365) == Time (1971, 1, 1, 12, 0, 0, 0, true));
+
+       #if ! JUCE_32BIT
         expect (Time (2038, 1, 1, 12, 0, 0, 0, true) + RelativeTime::days (365) == Time (2039, 1, 1, 12, 0, 0, 0, true));
+       #endif
 
         expect (Time (1982, 1, 1, 12, 0, 0, 0, false) + RelativeTime::days (365) == Time (1983, 1, 1, 12, 0, 0, 0, false));
         expect (Time (1970, 1, 1, 12, 0, 0, 0, false) + RelativeTime::days (365) == Time (1971, 1, 1, 12, 0, 0, 0, false));
diff --git a/modules/juce_osc/osc/juce_OSCTimeTag.cpp b/modules/juce_osc/osc/juce_OSCTimeTag.cpp
index be22dac060..d19f182607 100644
--- a/modules/juce_osc/osc/juce_OSCTimeTag.cpp
+++ b/modules/juce_osc/osc/juce_OSCTimeTag.cpp
@@ -126,7 +126,12 @@ public:
         }
         {
             Time currentTime (Time::currentTimeMillis());
-            double deltaInSeconds = 1.234;
+
+            // Make sure we use a double that has a representation that will always
+            // truncate to what we expect when multipled by 1000 and turned into
+            // integer milliseconds.
+            double deltaInSeconds = 1.562;
+
             RelativeTime delta (deltaInSeconds);
             Time laterTime = currentTime + delta;