diff --git a/pkg/compose/envresolver_fuzz_test.go b/pkg/compose/envresolver_fuzz_test.go
new file mode 100644
index 00000000000..b623f8ceb9f
--- /dev/null
+++ b/pkg/compose/envresolver_fuzz_test.go
@@ -0,0 +1,68 @@
+/*
+   Copyright 2020 Docker Compose CLI authors
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License.
+*/
+
+package compose
+
+import (
+	"strings"
+	"testing"
+)
+
+// FuzzEnvResolverWithCase locks the resolution semantics: the resolver is
+// exactly the map when case-sensitive, and an exact match must win over the
+// lower-cased fallback when case-insensitive.
+func FuzzEnvResolverWithCase(f *testing.F) {
+	f.Add("FOO", "bar", "BAZ", "qux", "foo")
+	f.Add("PATH", "/bin", "HOME", "/root", "path")
+	f.Fuzz(func(t *testing.T, k1, v1, k2, v2, query string) {
+		// keep the two keys distinct after case folding so the lower-cased
+		// fallback has a single unambiguous winner
+		if strings.EqualFold(k1, k2) {
+			k2 += "#"
+		}
+		environment := map[string]string{k1: v1, k2: v2}
+
+		// nil environment never resolves
+		if v, ok := envResolverWithCase(nil, true)(query); ok || v != "" {
+			t.Fatalf("nil environment must never resolve %q, got (%q, %t)", query, v, ok)
+		}
+
+		// case-sensitive: exactly the map
+		gotV, gotOK := envResolverWithCase(environment, false)(query)
+		if wantOK := query == k1 || query == k2; gotOK != wantOK || gotV != environment[query] {
+			t.Fatalf("case-sensitive resolver disagrees with the map for %q: got (%q, %t), want (%q, %t)",
+				query, gotV, gotOK, environment[query], wantOK)
+		}
+
+		// case-insensitive: exact match first, then lower-cased fallback
+		gotV, gotOK = envResolverWithCase(environment, true)(query)
+		wantV, wantOK := "", false
+		if query == k1 || query == k2 {
+			wantV, wantOK = environment[query], true
+		} else {
+			switch strings.ToLower(query) {
+			case strings.ToLower(k1):
+				wantV, wantOK = v1, true
+			case strings.ToLower(k2):
+				wantV, wantOK = v2, true
+			}
+		}
+		if gotV != wantV || gotOK != wantOK {
+			t.Fatalf("case-insensitive resolver for %q: got (%q, %t), want (%q, %t)",
+				query, gotV, gotOK, wantV, wantOK)
+		}
+	})
+}