diff --git a/cmd/config_helper.go b/cmd/config_helper.go
index e780f370..e4408cce 100644
--- a/cmd/config_helper.go
+++ b/cmd/config_helper.go
@@ -13,7 +13,11 @@ import (
 
 // makeId creates an opaque, deterministic string identifier, unique for each package present in the config.
 func makeId(pkg *api.Package) string {
-	return pkg.Name
+	id := pkg.Name
+	if pkg.Arch != "" {
+		id += "." + pkg.Arch
+	}
+	return id
 }
 
 func sortedKeys[K cmp.Ordered, V any](m map[K]V) []K {
diff --git a/pkg/sat/loader.go b/pkg/sat/loader.go
index 5d799966..e20bb68e 100644
--- a/pkg/sat/loader.go
+++ b/pkg/sat/loader.go
@@ -309,6 +309,9 @@ func (loader *Loader) explodeSamePackageConflicts(pkgVar *Var) bf.Formula {
 		if otherVar.Package == pkgVar.Package { // itself
 			continue
 		}
+		if otherVar.Package.Arch != pkgVar.Package.Arch {
+			continue
+		}
 		conflictingVars = append(conflictingVars, bf.Var(otherVar.satVarName))
 	}
 	if len(conflictingVars) == 0 {
diff --git a/pkg/sat/sat_test.go b/pkg/sat/sat_test.go
index a0a9fe87..d8fd6b12 100644
--- a/pkg/sat/sat_test.go
+++ b/pkg/sat/sat_test.go
@@ -1493,6 +1493,33 @@ func TestNewResolver(t *testing.T) {
 			exclude:       []string{"testb-0:1.x86_64"},
 			solvable:      true,
 		},
+		{name: "package needed in two architectures, and referenced by name", packages: []*api.Package{
+			newPkgAP("testa", "1", "i686", 1, []string{}, []string{"/usr/lib/libfoo.so"}, []string{}),
+			newPkgAP("testb", "1", "x86_64", 1, []string{}, []string{"/usr/lib64/libfoo.so"}, []string{}),
+			newPkgAP("testc", "1", "noarch", 1, []string{}, []string{"foo"}, []string{}),
+			newPkgAP("foo", "1", "i686", 1, []string{"/usr/lib/libfoo.so"}, []string{}, []string{}),
+			newPkgAP("foo", "1", "x86_64", 1, []string{"/usr/lib64/libfoo.so"}, []string{}, []string{}),
+		}, requires: []string{
+			"testa", "testb", "testc",
+		},
+			architectures: []string{"x86_64", "i686"},
+			install:       []string{"testa-0:1.i686", "testb-0:1.x86_64", "testc-0:1.noarch", "foo-0:1.i686", "foo-0:1.x86_64"},
+			exclude:       []string{},
+			solvable:      true,
+		},
+		{name: "package needed in two architectures, and referenced by file", packages: []*api.Package{
+			newPkgAP("testa", "1", "i686", 1, []string{}, []string{"/usr/lib/libfoo.so"}, []string{}),
+			newPkgAP("testb", "1", "x86_64", 1, []string{}, []string{"/usr/lib64/libfoo.so"}, []string{}),
+			newPkgAP("foo", "1", "i686", 1, []string{"/usr/lib/libfoo.so"}, []string{}, []string{}),
+			newPkgAP("foo", "1", "x86_64", 1, []string{"/usr/lib64/libfoo.so"}, []string{}, []string{}),
+		}, requires: []string{
+			"testa", "testb",
+		},
+			architectures: []string{"x86_64", "i686"},
+			install:       []string{"testa-0:1.i686", "testb-0:1.x86_64", "foo-0:1.i686", "foo-0:1.x86_64"},
+			exclude:       []string{},
+			solvable:      true,
+		},
 
 		// TODO: Add test cases.
 	}