diff --git a/src/cmd/go/internal/load/test.go b/src/cmd/go/internal/load/test.go
index eb8aef3ee2..374a2f9a4f 100644
--- a/src/cmd/go/internal/load/test.go
+++ b/src/cmd/go/internal/load/test.go
@@ -290,10 +290,12 @@ func TestPackagesAndErrors(ctx context.Context, p *Package, cover *TestCover) (p
 			seen[p1] = true
 		}
 		for _, p1 := range cover.Pkgs {
-			if !seen[p1] {
-				seen[p1] = true
-				pmain.Internal.Imports = append(pmain.Internal.Imports, p1)
+			if seen[p1] {
+				// Don't add duplicate imports.
+				continue
 			}
+			seen[p1] = true
+			pmain.Internal.Imports = append(pmain.Internal.Imports, p1)
 		}
 	}
 
diff --git a/src/cmd/go/internal/test/test.go b/src/cmd/go/internal/test/test.go
index ea9dfbe4e8..230ea2d318 100644
--- a/src/cmd/go/internal/test/test.go
+++ b/src/cmd/go/internal/test/test.go
@@ -716,6 +716,12 @@ func runTest(ctx context.Context, cmd *base.Command, args []string) {
 				}
 			}
 
+			// A package which only has test files can't be imported
+			// as a dependency, nor can it be instrumented for coverage.
+			if len(p.GoFiles)+len(p.CgoFiles) == 0 {
+				continue
+			}
+
 			// Silently ignore attempts to run coverage on
 			// sync/atomic when using atomic coverage mode.
 			// Atomic coverage mode uses sync/atomic, so
diff --git a/src/cmd/go/testdata/script/cover_pkgall_imports.txt b/src/cmd/go/testdata/script/cover_pkgall_imports.txt
new file mode 100644
index 0000000000..4e51726b29
--- /dev/null
+++ b/src/cmd/go/testdata/script/cover_pkgall_imports.txt
@@ -0,0 +1,48 @@
+# This test checks that -coverpkg=all can be used
+# when the package pattern includes packages
+# which only have tests.
+# Verifies golang.org/issue/27333, golang.org/issue/43242.
+
+[short] skip
+cd $GOPATH/src/example.com/cov
+
+env GO111MODULE=on
+go test -coverpkg=all ./...
+
+env GO111MODULE=off
+go test -coverpkg=all ./...
+
+-- $GOPATH/src/example.com/cov/go.mod --
+module example.com/cov
+
+-- $GOPATH/src/example.com/cov/notest/notest.go --
+package notest
+
+func Foo() {}
+
+-- $GOPATH/src/example.com/cov/onlytest/onlytest_test.go --
+package onlytest_test
+
+import (
+	"testing"
+
+	"example.com/cov/notest"
+)
+
+func TestFoo(t *testing.T) {
+	notest.Foo()
+}
+
+-- $GOPATH/src/example.com/cov/withtest/withtest.go --
+package withtest
+
+func Bar() {}
+
+-- $GOPATH/src/example.com/cov/withtest/withtest_test.go --
+package withtest
+
+import "testing"
+
+func TestBar(t *testing.T) {
+	Bar()
+}