diff --git a/doc/pages/Manual.md b/doc/pages/Manual.md
index 0f4929b6201..24cc4ed84ba 100644
--- a/doc/pages/Manual.md
+++ b/doc/pages/Manual.md
@@ -973,14 +973,18 @@ files.
   considered incompatible. This is useful to define sets of mutually conflicting
   packages.
 
-- <a id="opamfield-depexts">
-  `depexts: [ [ <string> ... ] { <filter> }  ... ]`</a>:
-  the package external dependencies. This field may be used to describe the
-  dependencies of the package toward software or packages external to the <span
-  class="opam">opam</span> ecosystem, for various systems. Each
-  `[ <string> ... ] { <filter> }` element declares the strings to the left as
-  identifiers to required system-managed packages, while the filter to the right
-  allows one to select the systems they will be active on.
+- <a id="opamfield-depexts"> `depexts: [ [ <string> ... ] { <filter> } ... ]`</a>:
+  the package external dependencies. This field is used to describe the
+  dependencies of the package toward packages external to the <span
+  class="opam">opam</span> ecosystem; <span class="opam">opam</span> will then
+  use its knowledge of the system package manager to determine the availability
+  of the package, and install these external dependencies on the system as
+  prerequisites of the package, asking the user for administrator rights if
+  required.
+
+    Each `[ <string> ... ] { <filter> }` element declares the strings to the
+    left as identifiers to required system-managed packages, while the filter to
+    the right allows one to select the systems they will be active on.
 
     The filters typically use variables [`arch`](#opamvar-arch),
     [`os`](#opamvar-os), [`os-distribution`](#opamvar-os-distribution),
diff --git a/master_changes.md b/master_changes.md
index e0a25fe4f2d..c149b490957 100644
--- a/master_changes.md
+++ b/master_changes.md
@@ -106,6 +106,7 @@ New option/command/subcommand are prefixed with ◈.
   * Improve messages to hint that answering `no` doesn't abort installation [#4591 @AltGr]
   * Add support for non-interactive mode in macports [#4676 @kit-ty-kate]
   * Handling of packages of tagged repositories for alpine [#4700 @rjbou - fix #4670]
+  * Clarify some `assume-depexts` related messages [#4671 @AltGr - partial fix #4662]
 
 ## Sandbox
   * Fix the conflict with the environment variable name used by dune [#4535 @smorimoto - fix ocaml/dune#4166]
diff --git a/src/state/opamSwitchState.ml b/src/state/opamSwitchState.ml
index 1f05a325a00..ffca58c1d53 100644
--- a/src/state/opamSwitchState.ml
+++ b/src/state/opamSwitchState.ml
@@ -1094,14 +1094,16 @@ let unavailable_reason st ?(default="") (name, vformula) =
       in
       let msg =
         match missing with
-        | [pkg] ->
-          " '" ^ pkg ^ "'"
+        | [pkg] -> " '" ^ pkg ^ "'"
         | pkgs ->
-          "s " ^ (OpamStd.Format.pretty_list (List.rev_map (Printf.sprintf "'%s'") pkgs))
+          "s " ^ (OpamStd.Format.pretty_list
+                    (List.rev_map (Printf.sprintf "'%s'") pkgs))
       in
       Printf.sprintf
         "depends on the unavailable system package%s. Use \
-         `--assume-depexts' to attempt installation anyway." msg
+         `--no-depexts' to attempt installation anyway, or it is \
+         possible that a depext package name in the opam file \
+         is incorrect." msg
     | None -> default
 
 let update_package_metadata nv opam st =