diff --git a/lib/lint.ml b/lib/lint.ml
index 067cb0e..bb9de21 100644
--- a/lib/lint.ml
+++ b/lib/lint.ml
@@ -231,7 +231,7 @@ module Checks = struct
       | OpamFormula.Atom (pkg, constr) ->
           if is_dune pkg then
             let v = get_lower_bound constr in
-            Some (Option.default "1.0" v)
+            Some (Option.default "" v)
           else None
       | Empty -> None
       | Block x -> aux x
@@ -249,10 +249,11 @@ module Checks = struct
           match (dune_constraint, dune_version) with
           | _, Error msg -> [ (pkg, FailedToDownload msg) ]
           | None, Ok None -> []
+          | Some "", _ -> [ (pkg, DuneLowerBoundMissing) ]
           | Some _, Ok None -> [ (pkg, DuneProjectMissing) ]
           | None, Ok (Some _) ->
               if is_dune (OpamPackage.name pkg) then []
-              else [ (pkg, DuneConstraintMissing) ]
+              else [ (pkg, DuneDependencyMissing) ]
           | Some dep, Ok (Some ver) ->
               if OpamVersionCompare.compare dep ver >= 0 then []
               else [ (pkg, BadDuneConstraint (dep, ver)) ]
diff --git a/lib/lint_error.ml b/lib/lint_error.ml
index 36e8f03..6122672 100644
--- a/lib/lint_error.ml
+++ b/lib/lint_error.ml
@@ -15,7 +15,8 @@ type error =
   | UnmatchedVersion of OpamPackage.Version.t
   | DubiousDuneSubst
   | DuneProjectMissing
-  | DuneConstraintMissing
+  | DuneDependencyMissing
+  | DuneLowerBoundMissing
   | DuneIsBuild
   | BadDuneConstraint of string * string
   | UnexpectedFile of string
@@ -99,11 +100,16 @@ let msg_of_error (package, (err : error)) =
         "Warning in %s: The package seems to use dune but the dune-project \
          file is missing."
         pkg
-  | DuneConstraintMissing ->
+  | DuneDependencyMissing ->
       Printf.sprintf
         "Warning in %s: The package has a dune-project file but no explicit \
          dependency on dune was found."
         pkg
+  | DuneLowerBoundMissing ->
+      Printf.sprintf
+        "Warning in %s: The package has a dune dependency without a lower \
+         bound."
+        pkg
   | BadDuneConstraint (dep, ver) ->
       Printf.sprintf
         "Error in %s: Your dune-project file indicates that this package \
diff --git a/test/lint.t b/test/lint.t
index 9870736..6402f4f 100644
--- a/test/lint.t
+++ b/test/lint.t
@@ -24,6 +24,9 @@ Setup repo for incorrect b package tests
   $ git apply "patches/b-incorrect-opam.patch"
   $ git add packages/
   $ echo "(lang dune 3.16)" > dune-project
+  $ sh "scripts/setup_sources.sh" b 0.0.2 dune-project
+  Created tarball b.0.0.2.tgz
+  Updated checksum for b.0.0.2.tgz in b.0.0.2's opam file
   $ sh "scripts/setup_sources.sh" b 0.0.3 dune-project
   Created tarball b.0.0.3.tgz
   Updated checksum for b.0.0.3.tgz in b.0.0.3's opam file
@@ -63,9 +66,8 @@ Test the following:
   Linting opam-repository at $TESTCASE_ROOT/. ...
   Warning in b.0.0.2: Dubious use of 'dune subst'. 'dune subst' should always only be called with {dev} (i.e. ["dune" "subst"] {dev}) If your opam file has been autogenerated by dune, you need to upgrade your dune-project to at least (lang dune 2.7).
   Warning in b.0.0.2: The package tagged dune as a build dependency. Due to a bug in dune (https://github.com/ocaml/dune/issues/2147) this should never be the case. Please remove the {build} tag from its filter.
-  Error in b.0.0.2: Failed to download the archive. Details: $TESTCASE_ROOT/b.0.0.2.tgz
+  Warning in b.0.0.2: The package has a dune dependency without a lower bound.
   Error in b.0.0.2:              error  3: File format error in 'unknown-field' at line 11, column 0: Invalid field unknown-field
-  Error in b.0.0.2:              error 60: Upstream check failed: "Source not found: $TESTCASE_ROOT/b.0.0.2.tgz"
   [1]
   $ opam-ci-check lint -r . -c b.0.0.3
   Linting opam-repository at $TESTCASE_ROOT/. ...