diff --git a/modules/juce_core/time/juce_Time.cpp b/modules/juce_core/time/juce_Time.cpp
index 4e2833a6a0..0e7d324aaa 100644
--- a/modules/juce_core/time/juce_Time.cpp
+++ b/modules/juce_core/time/juce_Time.cpp
@@ -435,19 +435,27 @@ String Time::toISO8601 (bool includeDividerCharacters) const
             + getUTCOffsetString (includeDividerCharacters);
 }
 
-static int parseFixedSizeIntAndSkip (String::CharPointerType& t, int numChars, char charToSkip) noexcept
+static int parseVariableSizeIntAndSkip (String::CharPointerType& t,
+                                        int minNumChars,
+                                        int targetNumChars,
+                                        char charToSkip) noexcept
 {
     int n = 0;
 
-    for (int i = numChars; --i >= 0;)
+    for (int i = 0; i < targetNumChars; ++i)
     {
-        auto digit = (int) (*t - '0');
+        n *= 10;
+        const auto digit = (int) (*t - '0');
 
-        if (! isPositiveAndBelow (digit, 10))
+        if (isPositiveAndBelow (digit, 10))
+        {
+            n += digit;
+            ++t;
+        }
+        else if (i < minNumChars)
+        {
             return -1;
-
-        ++t;
-        n = n * 10 + digit;
+        }
     }
 
     if (charToSkip != 0 && *t == (juce_wchar) charToSkip)
@@ -456,6 +464,11 @@ static int parseFixedSizeIntAndSkip (String::CharPointerType& t, int numChars, c
     return n;
 }
 
+static int parseFixedSizeIntAndSkip (String::CharPointerType& t, int numChars, char charToSkip) noexcept
+{
+    return parseVariableSizeIntAndSkip (t, numChars, numChars, charToSkip);
+}
+
 Time Time::fromISO8601 (StringRef iso)
 {
     auto t = iso.text;
@@ -515,13 +528,16 @@ Time Time::fromISO8601 (StringRef iso)
         if (*t == '.' || *t == ',')
         {
             ++t;
-            milliseconds = parseFixedSizeIntAndSkip (t, 3, 0);
+            milliseconds = parseVariableSizeIntAndSkip (t, 1, 3, 0);
 
             if (milliseconds < 0)
             {
                 jassertfalse;
                 return {};
             }
+
+            // skip to the next non-digit character
+            while (t.isDigit()) { ++t; }
         }
 
         milliseconds += 1000 * seconds;
@@ -701,6 +717,46 @@ public:
         expect (Time::fromISO8601 ("20160216T150357.999-0230")      == Time (2016, 1, 16, 17, 33, 57, 999, false));
         expect (Time::fromISO8601 ("20160216T150357,999-0230")      == Time (2016, 1, 16, 17, 33, 57, 999, false));
 
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57.9+00:00") == Time (2016, 1, 16, 15, 3, 57, 900, false));
+        expect (Time::fromISO8601 ("20160216T150357.9+0000")      == Time (2016, 1, 16, 15, 3, 57, 900, false));
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57.9Z")      == Time (2016, 1, 16, 15, 3, 57, 900, false));
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57,9Z")      == Time (2016, 1, 16, 15, 3, 57, 900, false));
+        expect (Time::fromISO8601 ("20160216T150357.9Z")          == Time (2016, 1, 16, 15, 3, 57, 900, false));
+        expect (Time::fromISO8601 ("20160216T150357,9Z")          == Time (2016, 1, 16, 15, 3, 57, 900, false));
+
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57.9-02:30") == Time (2016, 1, 16, 17, 33, 57, 900, false));
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57,9-02:30") == Time (2016, 1, 16, 17, 33, 57, 900, false));
+        expect (Time::fromISO8601 ("20160216T150357.9-0230")      == Time (2016, 1, 16, 17, 33, 57, 900, false));
+        expect (Time::fromISO8601 ("20160216T150357,9-0230")      == Time (2016, 1, 16, 17, 33, 57, 900, false));
+
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57.99+00:00") == Time (2016, 1, 16, 15, 3, 57, 990, false));
+        expect (Time::fromISO8601 ("20160216T150357.99+0000")      == Time (2016, 1, 16, 15, 3, 57, 990, false));
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57.99Z")      == Time (2016, 1, 16, 15, 3, 57, 990, false));
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57,99Z")      == Time (2016, 1, 16, 15, 3, 57, 990, false));
+        expect (Time::fromISO8601 ("20160216T150357.99Z")          == Time (2016, 1, 16, 15, 3, 57, 990, false));
+        expect (Time::fromISO8601 ("20160216T150357,99Z")          == Time (2016, 1, 16, 15, 3, 57, 990, false));
+
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57.99-02:30") == Time (2016, 1, 16, 17, 33, 57, 990, false));
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57,99-02:30") == Time (2016, 1, 16, 17, 33, 57, 990, false));
+        expect (Time::fromISO8601 ("20160216T150357.99-0230")      == Time (2016, 1, 16, 17, 33, 57, 990, false));
+        expect (Time::fromISO8601 ("20160216T150357,99-0230")      == Time (2016, 1, 16, 17, 33, 57, 990, false));
+
+        // The 8601 standard appears to support any number of fractional digits.
+        // The fractional part should either be rounded or truncated.
+        // The Time class stores time with millisecond precision.
+        // Most implementations appear to truncate so that's what we test for too.
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57.9999+00:00") == Time (2016, 1, 16, 15, 3, 57, 999, false));
+        expect (Time::fromISO8601 ("20160216T150357.999999999+0000") == Time (2016, 1, 16, 15, 3, 57, 999, false));
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57.999999999Z") == Time (2016, 1, 16, 15, 3, 57, 999, false));
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57,999999999Z") == Time (2016, 1, 16, 15, 3, 57, 999, false));
+        expect (Time::fromISO8601 ("20160216T150357.9999999999999Z") == Time (2016, 1, 16, 15, 3, 57, 999, false));
+        expect (Time::fromISO8601 ("20160216T150357,9999999999999Z") == Time (2016, 1, 16, 15, 3, 57, 999, false));
+
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57.9999-02:30") == Time (2016, 1, 16, 17, 33, 57, 999, false));
+        expect (Time::fromISO8601 ("2016-02-16T15:03:57,9999-02:30") == Time (2016, 1, 16, 17, 33, 57, 999, false));
+        expect (Time::fromISO8601 ("20160216T150357.999999999-0230") == Time (2016, 1, 16, 17, 33, 57, 999, false));
+        expect (Time::fromISO8601 ("20160216T150357,999999999-0230") == Time (2016, 1, 16, 17, 33, 57, 999, false));
+
         expect (Time (1970,  0,  1,  0,  0,  0, 0, false) == Time (0));
         expect (Time (2106,  1,  7,  6, 28, 15, 0, false) == Time (4294967295000));
         expect (Time (2007, 10,  7,  1,  7, 20, 0, false) == Time (1194397640000));