diff --git a/library/std/src/os/unix/process.rs b/library/std/src/os/unix/process.rs
index d95bc9b15c9c4..d5132375a257a 100644
--- a/library/std/src/os/unix/process.rs
+++ b/library/std/src/os/unix/process.rs
@@ -21,6 +21,13 @@ pub trait CommandExt: Sealed {
     /// Sets the child process's user ID. This translates to a
     /// `setuid` call in the child process. Failure in the `setuid`
     /// call will cause the spawn to fail.
+    ///
+    /// # Notes
+    ///
+    /// This will also trigger a call to `setgroups(0, NULL)` in the child
+    /// process if no groups have been specified.
+    /// This removes supplementary groups that might have given the child
+    /// unwanted permissions.
     #[stable(feature = "rust1", since = "1.0.0")]
     fn uid(
         &mut self,
diff --git a/library/std/src/sys/unix/process/process_unix.rs b/library/std/src/sys/unix/process/process_unix.rs
index 3d305cd7310fd..625d0526a59b6 100644
--- a/library/std/src/sys/unix/process/process_unix.rs
+++ b/library/std/src/sys/unix/process/process_unix.rs
@@ -304,14 +304,22 @@ impl Command {
             if let Some(u) = self.get_uid() {
                 // When dropping privileges from root, the `setgroups` call
                 // will remove any extraneous groups. We only drop groups
-                // if the current uid is 0 and we weren't given an explicit
+                // if we have CAP_SETGID and we weren't given an explicit
                 // set of groups. If we don't call this, then even though our
                 // uid has dropped, we may still have groups that enable us to
                 // do super-user things.
                 //FIXME: Redox kernel does not support setgroups yet
                 #[cfg(not(target_os = "redox"))]
-                if libc::getuid() == 0 && self.get_groups().is_none() {
-                    cvt(libc::setgroups(0, ptr::null()))?;
+                if self.get_groups().is_none() {
+                    let res = cvt(libc::setgroups(0, ptr::null()));
+                    if let Err(e) = res {
+                        // Here we ignore the case of not having CAP_SETGID.
+                        // An alternative would be to require CAP_SETGID (in
+                        // addition to CAP_SETUID) for setting the UID.
+                        if e.raw_os_error() != Some(libc::EPERM) {
+                            return Err(e.into());
+                        }
+                    }
                 }
                 cvt(libc::setuid(u as uid_t))?;
             }