diff --git a/Lib/idlelib/NEWS.txt b/Lib/idlelib/NEWS.txt
index 7646aed..64636df 100644
--- a/Lib/idlelib/NEWS.txt
+++ b/Lib/idlelib/NEWS.txt
@@ -3,6 +3,9 @@
 ======================================
 
 
+bpo-37321: Both subprocess connection error messages now refer to
+the 'Startup failure' section of the IDLE doc.
+
 bpo-37039: Adjust "Zoom Height" to individual screens by momemtarily
 maximizing the window on first use with a particular screen.  Changing
 screen settings may invalidate the saved height.  While a window is
diff --git a/Lib/idlelib/pyshell.py b/Lib/idlelib/pyshell.py
index 6e0707d..7ad5a76 100755
--- a/Lib/idlelib/pyshell.py
+++ b/Lib/idlelib/pyshell.py
@@ -824,10 +824,10 @@
 
     def display_no_subprocess_error(self):
         tkMessageBox.showerror(
-            "Subprocess Startup Error",
-            "IDLE's subprocess didn't make connection.  Either IDLE can't "
-            "start a subprocess or personal firewall software is blocking "
-            "the connection.",
+            "Subprocess Connection Error",
+            "IDLE's subprocess didn't make connection.\n"
+            "See the 'Startup failure' section of the IDLE doc, online at\n"
+            "https://docs.python.org/3/library/idle.html#startup-failure",
             parent=self.tkconsole.text)
 
     def display_executing_dialog(self):
diff --git a/Lib/idlelib/run.py b/Lib/idlelib/run.py
index 4075dee..6b3928b 100644
--- a/Lib/idlelib/run.py
+++ b/Lib/idlelib/run.py
@@ -199,11 +199,13 @@
     root = tkinter.Tk()
     fix_scaling(root)
     root.withdraw()
-    msg = f"IDLE's subprocess can't connect to {address[0]}:{address[1]}.\n"\
-          f"Fatal OSError #{err.errno}: {err.strerror}.\n"\
-          f"See the 'Startup failure' section of the IDLE doc, online at\n"\
-          f"https://docs.python.org/3/library/idle.html#startup-failure"
-    showerror("IDLE Subprocess Error", msg, parent=root)
+    showerror(
+            "Subprocess Connection Error",
+            f"IDLE's subprocess can't connect to {address[0]}:{address[1]}.\n"
+            f"Fatal OSError #{err.errno}: {err.strerror}.\n"
+            "See the 'Startup failure' section of the IDLE doc, online at\n"
+            "https://docs.python.org/3/library/idle.html#startup-failure",
+            parent=root)
     root.destroy()
 
 def print_exception():
diff --git a/Misc/NEWS.d/next/IDLE/2019-06-17-16-35-30.bpo-37321.zVTTGS.rst b/Misc/NEWS.d/next/IDLE/2019-06-17-16-35-30.bpo-37321.zVTTGS.rst
new file mode 100644
index 0000000..1321986
--- /dev/null
+++ b/Misc/NEWS.d/next/IDLE/2019-06-17-16-35-30.bpo-37321.zVTTGS.rst
@@ -0,0 +1,2 @@
+Both subprocess connection error messages now refer to the 'Startup failure'
+section of the IDLE doc.