diff --git a/core/src/main/java/hudson/scheduler/CronTab.java b/core/src/main/java/hudson/scheduler/CronTab.java
index 72614b3921902d24c983d9b713a2c30e45a50530..ec8c4ffb430aa0d3d7915ad0eac9b79a37547ac9 100644
--- a/core/src/main/java/hudson/scheduler/CronTab.java
+++ b/core/src/main/java/hudson/scheduler/CronTab.java
@@ -29,6 +29,8 @@ import java.io.StringReader;
 import java.util.Calendar;
 import java.util.GregorianCalendar;
 import java.util.Locale;
+import java.util.regex.Matcher;
+import java.util.regex.Pattern;
 
 import static java.util.Calendar.*;
 import javax.annotation.CheckForNull;
@@ -451,6 +453,19 @@ public final class CronTab {
         } else if (spec.matches("\\d+ .+")) {// "0 ..." (certain minute) to hash
             return "H " + spec.substring(spec.indexOf(' ') + 1);
         } else {
+            Matcher m = Pattern.compile("0(,(\\d+)(,\\d+)*)( .+)").matcher(spec);
+            if (m.matches()) { // 0,15,30,45 to H/15
+                int period = Integer.parseInt(m.group(2));
+                if (period > 0) {
+                    StringBuilder b = new StringBuilder();
+                    for (int i = period; i < 60; i += period) {
+                        b.append(',').append(i);
+                    }
+                    if (b.toString().equals(m.group(1))) {
+                        return "H/" + period + m.group(4);
+                    }
+                }
+            }
             return null;
         }
     }
diff --git a/core/src/test/java/hudson/scheduler/CronTabTest.java b/core/src/test/java/hudson/scheduler/CronTabTest.java
index c7d943fbee2150ba38ba32d5fbe7e17e0a506e5b..388784b141a19222c37829a3c1bbabc16ece3e39 100644
--- a/core/src/test/java/hudson/scheduler/CronTabTest.java
+++ b/core/src/test/java/hudson/scheduler/CronTabTest.java
@@ -176,6 +176,7 @@ public class CronTabTest {
     @Test public void checkSanity() throws Exception {
         assertEquals(null, new CronTab("@hourly").checkSanity());
         assertEquals(Messages.CronTab_do_you_really_mean_every_minute_when_you("* * * * *", "H * * * *"), new CronTab("* * * * *").checkSanity());
+        assertEquals(Messages.CronTab_do_you_really_mean_every_minute_when_you("*/1 * * * *", "H * * * *"), new CronTab("*/1 * * * *").checkSanity());
         assertEquals(null, new CronTab("H H(0-2) * * *", Hash.from("stuff")).checkSanity());
         assertEquals(Messages.CronTab_do_you_really_mean_every_minute_when_you("* 0 * * *", "H 0 * * *"), new CronTab("* 0 * * *").checkSanity());
         assertEquals(Messages.CronTab_do_you_really_mean_every_minute_when_you("* 6,18 * * *", "H 6,18 * * *"), new CronTab("* 6,18 * * *").checkSanity());
@@ -183,11 +184,12 @@ public class CronTabTest {
         assertEquals(Messages.CronTab_do_you_really_mean_every_minute_when_you("* * 3 * *", "H * 3 * *"), new CronTab("* * 3 * *").checkSanity());
         // promote hashes:
         assertEquals(Messages.CronTab_spread_load_evenly_by_using_rather_than_("H/15 * * * *", "*/15 * * * *"), new CronTab("*/15 * * * *").checkSanity());
-        // XXX 0,15,30,45 * * * * → H/15 * * * *
+        assertEquals(Messages.CronTab_spread_load_evenly_by_using_rather_than_("H/15 * * * *", "0,15,30,45 * * * *"), new CronTab("0,15,30,45 * * * *").checkSanity());
         assertEquals(Messages.CronTab_spread_load_evenly_by_using_rather_than_("H * * * *", "0 * * * *"), new CronTab("0 * * * *").checkSanity());
+        assertEquals(Messages.CronTab_spread_load_evenly_by_using_rather_than_("H * * * *", "5 * * * *"), new CronTab("5 * * * *").checkSanity());
         // if the user specifically asked for 3:00 AM, probably we should stick to 3:00–3:59
         assertEquals(Messages.CronTab_spread_load_evenly_by_using_rather_than_("H 3 * * *", "0 3 * * *"), new CronTab("0 3 * * *").checkSanity());
-
+        assertEquals(Messages.CronTab_spread_load_evenly_by_using_rather_than_("H 22 * * 6", "00 22 * * 6"), new CronTab("00 22 * * 6").checkSanity());
         assertEquals(null, new CronTab("H/15 * 1 1 *").checkSanity());
     }