diff --git a/internal/setup/setup.go b/internal/setup/setup.go
index 10953ada..f8e86f94 100644
--- a/internal/setup/setup.go
+++ b/internal/setup/setup.go
@@ -153,6 +153,9 @@ func (s *Slice) String() string { return s.Package + "_" + s.Name }
 type Selection struct {
 	Release *Release
 	Slices  []*Slice
+	// Arch is the architecture the selection was made for. Paths listed for
+	// other architectures do not take part in it.
+	Arch string
 }
 
 // Prefers uses the prefer relationships and returns a map from each path to
@@ -166,7 +169,10 @@ func (s *Selection) Prefers() (map[string]*Package, error) {
 
 	pathPreferredPkg := make(map[string]*Package)
 	for _, slice := range s.Slices {
-		for path := range slice.Contents {
+		for path, info := range slice.Contents {
+			if len(info.Arch) > 0 && s.Arch != "" && !slices.Contains(info.Arch, s.Arch) {
+				continue
+			}
 			_, hasPrefers := prefers[preferKey{preferSource, path, ""}]
 			if !hasPrefers {
 				continue
@@ -482,6 +488,7 @@ func Select(release *Release, slices []SliceKey, arch string) (*Selection, error
 
 	selection := &Selection{
 		Release: release,
+		Arch:    arch,
 	}
 
 	sorted, err := order(release.Packages, slices, arch)
diff --git a/internal/setup/setup_test.go b/internal/setup/setup_test.go
index ec61490b..4b742fba 100644
--- a/internal/setup/setup_test.go
+++ b/internal/setup/setup_test.go
@@ -428,6 +428,7 @@ var setupTests = []setupTest{{
 	},
 	selslices: []setup.SliceKey{{"mypkg1", "myslice1"}},
 	selection: &setup.Selection{
+		Arch: "amd64",
 		Slices: []*setup.Slice{{
 			Package: "mypkg1",
 			Name:    "myslice1",
@@ -451,6 +452,7 @@ var setupTests = []setupTest{{
 	},
 	selslices: []setup.SliceKey{{"mypkg2", "myslice2"}},
 	selection: &setup.Selection{
+		Arch: "amd64",
 		Slices: []*setup.Slice{{
 			Package: "mypkg1",
 			Name:    "myslice1",
@@ -1891,6 +1893,7 @@ var setupTests = []setupTest{{
 	},
 	selslices: []setup.SliceKey{{"mypkg", "myslice"}},
 	selection: &setup.Selection{
+		Arch: "amd64",
 		Slices: []*setup.Slice{{
 			Package: "mypkg",
 			Name:    "myslice",
@@ -2729,6 +2732,31 @@ var setupTests = []setupTest{{
 		"/path": "mypkg2",
 		"/link": "mypkg1",
 	},
+}, {
+	summary: "Path 'prefer' ignores packages listing the path for another arch",
+	selslices: []setup.SliceKey{
+		{"mypkg1", "myslice1"},
+		{"mypkg2", "myslice1"},
+	},
+	input: map[string]string{
+		"slices/mydir/mypkg1.yaml": `
+			package: mypkg1
+			slices:
+				myslice1:
+					contents:
+						/path: {arch: arm64}
+		`,
+		"slices/mydir/mypkg2.yaml": `
+			package: mypkg2
+			slices:
+				myslice1:
+					contents:
+						/path: {prefer: mypkg1}
+		`,
+	},
+	prefers: map[string]string{
+		"/path": "mypkg2",
+	},
 }, {
 	summary: "Cannot specify same package in 'prefer'",
 	input: map[string]string{
diff --git a/internal/slicer/slicer_test.go b/internal/slicer/slicer_test.go
index d6ef9ca0..abb3a926 100644
--- a/internal/slicer/slicer_test.go
+++ b/internal/slicer/slicer_test.go
@@ -1868,6 +1868,50 @@ var slicerTests = []slicerTest{{
 		"/link": "symlink /file1 {test-package1_myslice}",
 		"/text": "file 0644 2c26b46b {test-package1_myslice}",
 	},
+}, {
+	summary: "Preferred package lists the path only for another arch",
+	arch:    "i386",
+	slices: []setup.SliceKey{
+		{"test-package1", "myslice"},
+		{"test-package2", "myslice"},
+	},
+	pkgs: []*testutil.TestPackage{{
+		Name: "test-package1",
+		Data: testutil.MustMakeDeb([]testutil.TarEntry{
+			testutil.Dir(0755, "./"),
+			testutil.Reg(0644, "./file", "foo"),
+		}),
+	}, {
+		Name: "test-package2",
+		Data: testutil.MustMakeDeb([]testutil.TarEntry{
+			testutil.Dir(0755, "./"),
+			testutil.Reg(0644, "./file", "bar"),
+		}),
+	}},
+	release: map[string]string{
+		"slices/mydir/test-package1.yaml": `
+			package: test-package1
+			slices:
+				myslice:
+					contents:
+						/file: {arch: amd64}
+		`,
+		"slices/mydir/test-package2.yaml": `
+			package: test-package2
+			slices:
+				myslice:
+					contents:
+						/file: {prefer: test-package1}
+		`,
+	},
+	// test-package1 does not list /file for i386, so test-package2 is the
+	// only package providing it and must extract it.
+	filesystem: map[string]string{
+		"/file": "file 0644 fcde2b2e",
+	},
+	manifestPaths: map[string]string{
+		"/file": "file 0644 fcde2b2e {test-package2_myslice}",
+	},
 }, {
 	summary: "Warning when implicit parent directories conflict",
 	slices: []setup.SliceKey{