diff --git a/docs/scheduler/coordinator.md b/docs/scheduler/coordinator.md
index 5118956f..043c34b9 100644
--- a/docs/scheduler/coordinator.md
+++ b/docs/scheduler/coordinator.md
@@ -493,7 +493,8 @@ caps. swarm-controller alone writes it:
 
 `PUT` refuses an agent no hive's wanted state declares, unknown fields, and
 any value systemd would ignore, which would leave the agent uncapped. A
-percentage has at most two decimals and is above zero, up to `100%` for
+percentage has at most two decimals, no leading zero in its whole part (it
+refuses `08%`), and is above zero, up to `100%` for
 `memory_max` and `21474836.47%` for `cpu_quota`. A size is digits with an
 optional fraction and an optional `B`, `K`, `M`, `G` or `T` (upper case), at
 least one byte and below 2^64 - 1 bytes. The controller stores each value as
diff --git a/swarm-controller/src/agent_limits.rs b/swarm-controller/src/agent_limits.rs
index 3d33a900..90351ab3 100644
--- a/swarm-controller/src/agent_limits.rs
+++ b/swarm-controller/src/agent_limits.rs
@@ -105,7 +105,9 @@ fn memory_max(value: &str) -> Result<String, String> {
 }
 
 /// `value` as systemd reads a percentage, in hundredths of a percent: digits,
-/// optionally `.` and one or two digits, then `%`. `None` for anything else.
+/// optionally `.` and one or two digits, then `%`. `None` for anything else,
+/// and for a whole part with a leading zero other than `0` itself: systemd
+/// ignores `08%` and may read `010%` as octal.
 fn hundredths(value: &str) -> Option<u64> {
     let number = value.strip_suffix('%')?;
     let (int, frac) = match number.split_once('.') {
@@ -113,7 +115,7 @@ fn hundredths(value: &str) -> Option<u64> {
         Some(_) => return None,
         None => (number, ""),
     };
-    if !digits(int) {
+    if !digits(int) || (int.len() > 1 && int.starts_with('0')) {
         return None;
     }
     let frac = match frac.len() {
@@ -324,7 +326,6 @@ mod tests {
             "0.01%",
             "1500%",
             "400.12%",
-            "05%",
             "21474836.47%",
         ] {
             assert_eq!(cpu_quota(ok).as_deref(), Ok(ok));
@@ -345,6 +346,11 @@ mod tests {
             "0.001%",
             "99999999999999999999%",
             "21474836.48%",
+            "05%",
+            "08%",
+            "085480%",
+            "010%",
+            "00.5%",
             "1.%",
             ".5%",
             "400%\nExecStartPre=/bin/sh -c id #%",
@@ -391,6 +397,10 @@ mod tests {
             "150%",
             "100.01%",
             "12.345%",
+            "08%",
+            "085480%",
+            "010%",
+            "00.5%",
             "8X",
             "G",
             "8 G",