diff --git a/README.md b/README.md
index 073a52e..2ec95d5 100644
--- a/README.md
+++ b/README.md
@@ -52,7 +52,7 @@ settings.
 
  * Index verification via jar signature - currently relies on HTTPS
  * Interaction with multiple devices at once
- * Device compatibility filters (minSdk, maxSdk, arch, hardware features)
+ * Hardware features filtering
 
 ### Advantages over the Android client
 
diff --git a/cmd/fdroidcl/download.go b/cmd/fdroidcl/download.go
index ece7c64..91a87a9 100644
--- a/cmd/fdroidcl/download.go
+++ b/cmd/fdroidcl/download.go
@@ -26,12 +26,14 @@ func runDownload(args []string) {
 	}
 	apps := findApps(args)
 	for _, app := range apps {
-		apk := app.CurApk()
-		if apk == nil {
-			log.Fatalf("No current apk found for %s", app.ID)
+		apks := app.SuggestedApks()
+		if len(apks) == 0 {
+			log.Fatalf("No suggested APKs found for %s", app.ID)
+		}
+		for _, apk := range apks {
+			path := downloadApk(&apk)
+			fmt.Printf("APK available in %s\n", path)
 		}
-		path := downloadApk(apk)
-		fmt.Printf("APK available in %s\n", path)
 	}
 }
 
diff --git a/cmd/fdroidcl/install.go b/cmd/fdroidcl/install.go
index 0835950..83b0e18 100644
--- a/cmd/fdroidcl/install.go
+++ b/cmd/fdroidcl/install.go
@@ -43,9 +43,9 @@ func downloadAndDo(apps []*fdroidcl.App, device *adb.Device, doApk func(*adb.Dev
 	}
 	toInstall := make([]downloaded, len(apps))
 	for i, app := range apps {
-		apk := app.CurApk()
+		apk := app.SuggestedApk(device)
 		if apk == nil {
-			log.Fatalf("No current apk found for %s", app.ID)
+			log.Fatalf("No suitable APKs found for %s", app.ID)
 		}
 		path := downloadApk(apk)
 		toInstall[i] = downloaded{apk: apk, path: path}
diff --git a/cmd/fdroidcl/search.go b/cmd/fdroidcl/search.go
index 83af8eb..2c4d202 100644
--- a/cmd/fdroidcl/search.go
+++ b/cmd/fdroidcl/search.go
@@ -48,12 +48,11 @@ func runSearch(args []string) {
 		device = mustOneDevice()
 	}
 	apps := filterAppsSearch(mustLoadIndexes(), args)
-	instPkgs := mustInstalled(device)
 	if *installed {
-		apps = filterAppsInstalled(apps, instPkgs)
+		apps = filterAppsInstalled(apps, device)
 	}
 	if *updates {
-		apps = filterAppsUpdates(apps, instPkgs)
+		apps = filterAppsUpdates(apps, device)
 	}
 	if *category != "" {
 		apps = filterAppsCategory(apps, *category)
@@ -70,7 +69,7 @@ func runSearch(args []string) {
 			fmt.Println(app.ID)
 		}
 	} else {
-		printApps(apps, instPkgs)
+		printApps(apps, device)
 	}
 }
 
@@ -108,44 +107,41 @@ fieldLoop:
 	return false
 }
 
-func printApps(apps []fdroidcl.App, inst map[string]adb.Package) {
+func printApps(apps []fdroidcl.App, device *adb.Device) {
 	maxIDLen := 0
 	for _, app := range apps {
 		if len(app.ID) > maxIDLen {
 			maxIDLen = len(app.ID)
 		}
 	}
+	inst := mustInstalled(device)
 	for _, app := range apps {
 		var pkg *adb.Package
 		p, e := inst[app.ID]
 		if e {
 			pkg = &p
 		}
-		printApp(app, maxIDLen, pkg)
+		printApp(app, maxIDLen, pkg, device)
 	}
 }
 
-func descVersion(app fdroidcl.App, inst *adb.Package) string {
-	cur := app.CurApk()
-	if cur == nil {
-		return "(no version available)"
-	}
-	if inst == nil {
-		return fmt.Sprintf("%s (%d)", cur.VName, cur.VCode)
-	}
-	if inst.VCode < cur.VCode {
-		return fmt.Sprintf("%s (%d) -> %s (%d)", inst.VName, inst.VCode,
-			cur.VName, cur.VCode)
-	}
-	if !*installed {
-		return fmt.Sprintf("%s (%d) [installed]", cur.VName, cur.VCode)
+func descVersion(app fdroidcl.App, inst *adb.Package, device *adb.Device) string {
+	// With "-u" or "-i" option there must be a connected device
+	if *updates || *installed {
+		suggested := app.SuggestedApk(device)
+		if suggested != nil && inst.VCode < suggested.VCode {
+			return fmt.Sprintf("%s (%d) -> %s (%d)", inst.VName, inst.VCode,
+				suggested.VName, suggested.VCode)
+		}
+		return fmt.Sprintf("%s (%d)", inst.VName, inst.VCode)
 	}
-	return fmt.Sprintf("%s (%d)", cur.VName, cur.VCode)
+	// Without "-u" or "-i" we only have repositories indices
+	return fmt.Sprintf("%s (%d)", app.CVName, app.CVCode)
 }
 
-func printApp(app fdroidcl.App, IDLen int, inst *adb.Package) {
+func printApp(app fdroidcl.App, IDLen int, inst *adb.Package, device *adb.Device) {
 	fmt.Printf("%s%s %s - %s\n", app.ID, strings.Repeat(" ", IDLen-len(app.ID)),
-		app.Name, descVersion(app, inst))
+		app.Name, descVersion(app, inst, device))
 	fmt.Printf("    %s\n", app.Summary)
 }
 
@@ -160,8 +156,9 @@ func mustInstalled(device *adb.Device) map[string]adb.Package {
 	return inst
 }
 
-func filterAppsInstalled(apps []fdroidcl.App, inst map[string]adb.Package) []fdroidcl.App {
+func filterAppsInstalled(apps []fdroidcl.App, device *adb.Device) []fdroidcl.App {
 	var result []fdroidcl.App
+	inst := mustInstalled(device)
 	for _, app := range apps {
 		if _, e := inst[app.ID]; !e {
 			continue
@@ -171,18 +168,19 @@ func filterAppsInstalled(apps []fdroidcl.App, inst map[string]adb.Package) []fdr
 	return result
 }
 
-func filterAppsUpdates(apps []fdroidcl.App, inst map[string]adb.Package) []fdroidcl.App {
+func filterAppsUpdates(apps []fdroidcl.App, device *adb.Device) []fdroidcl.App {
 	var result []fdroidcl.App
+	inst := mustInstalled(device)
 	for _, app := range apps {
 		p, e := inst[app.ID]
 		if !e {
 			continue
 		}
-		cur := app.CurApk()
-		if cur == nil {
+		suggested := app.SuggestedApk(device)
+		if suggested == nil {
 			continue
 		}
-		if p.VCode >= cur.VCode {
+		if p.VCode >= suggested.VCode {
 			continue
 		}
 		result = append(result, app)
diff --git a/cmd/fdroidcl/show.go b/cmd/fdroidcl/show.go
index 3e5aaed..708ce4d 100644
--- a/cmd/fdroidcl/show.go
+++ b/cmd/fdroidcl/show.go
@@ -69,13 +69,7 @@ func printAppDetailed(app fdroidcl.App) {
 	p("Summary          :", "%s", app.Summary)
 	p("Added            :", "%s", app.Added.String())
 	p("Last Updated     :", "%s", app.Updated.String())
-	cur := app.CurApk()
-	if cur != nil {
-		p("Current Version  :", "%s (%d)", cur.VName, cur.VCode)
-	} else {
-		p("Current Version  :", "(no version available)")
-	}
-	p("Upstream Version :", "%s (%d)", app.CVName, app.CVCode)
+	p("Version          :", "%s (%d)", app.CVName, app.CVCode)
 	p("License          :", "%s", app.License)
 	if app.Categs != nil {
 		p("Categories       :", "%s", strings.Join(app.Categs, ", "))
diff --git a/cmd/fdroidcl/upgrade.go b/cmd/fdroidcl/upgrade.go
index 68bf633..bc33029 100644
--- a/cmd/fdroidcl/upgrade.go
+++ b/cmd/fdroidcl/upgrade.go
@@ -33,8 +33,11 @@ func runUpgrade(args []string) {
 		if !e {
 			log.Fatalf("%s is not installed", app.ID)
 		}
-		cur := app.CurApk()
-		if p.VCode >= cur.VCode {
+		suggested := app.SuggestedApk(device)
+		if suggested == nil {
+			log.Fatalf("No suitable APKs found for %s", app.ID)
+		}
+		if p.VCode >= suggested.VCode {
 			log.Fatalf("%s is up to date", app.ID)
 		}
 	}
diff --git a/index.go b/index.go
index 6853c59..ad80bd1 100644
--- a/index.go
+++ b/index.go
@@ -9,6 +9,8 @@ import (
 	"io"
 	"sort"
 	"strings"
+
+	"github.com/mvdan/adb"
 )
 
 type Index struct {
@@ -81,11 +83,11 @@ func getIconsDir(density IconDensity) string {
 }
 
 func (a *App) IconURLForDensity(density IconDensity) string {
-	cur := a.CurApk()
-	if cur == nil {
+	if len(a.Apks) == 0 {
 		return ""
 	}
-	return fmt.Sprintf("%s/%s/%s", cur.Repo.URL, getIconsDir(density), a.Icon)
+	return fmt.Sprintf("%s/%s/%s", a.Apks[0].Repo.URL,
+		getIconsDir(density), a.Icon)
 }
 
 func (a *App) IconURL() string {
@@ -209,6 +211,29 @@ func (a *Apk) SrcURL() string {
 	return fmt.Sprintf("%s/%s", a.Repo.URL, a.SrcName)
 }
 
+func (apk *Apk) IsCompatibleABI(ABIs []string) bool {
+	if len(apk.ABIs) == 0 {
+		return true // APK does not contain native code
+	}
+	for i := range apk.ABIs {
+		for j := range ABIs {
+			if apk.ABIs[i] == ABIs[j] {
+				return true
+			}
+		}
+	}
+	return false
+}
+
+func (apk *Apk) IsCompatibleAPILevel(sdk int) bool {
+	return sdk >= apk.MinSdk && (apk.MaxSdk == 0 || sdk <= apk.MaxSdk)
+}
+
+func (apk *Apk) IsCompatible(device *adb.Device) bool {
+	return apk.IsCompatibleABI(device.ABIs) &&
+		apk.IsCompatibleAPILevel(device.APILevel)
+}
+
 type AppList []App
 
 func (al AppList) Len() int           { return len(al) }
@@ -242,15 +267,56 @@ func LoadIndexXML(r io.Reader) (*Index, error) {
 	return &index, nil
 }
 
-func (a *App) CurApk() *Apk {
+func (a *App) ApksByVName(vname string) []Apk {
+	var apks []Apk
 	for i := range a.Apks {
-		apk := a.Apks[i]
+		if vname == a.Apks[i].VName {
+			apks = append(apks, a.Apks[i])
+		}
+	}
+	return apks
+}
+
+func (a *App) SuggestedVName() string {
+	for i := range a.Apks {
+		apk := &a.Apks[i]
 		if a.CVCode >= apk.VCode {
-			return &apk
+			return apk.VName
+		}
+	}
+	return ""
+}
+
+func (a *App) SuggestedApks() []Apk {
+	// No APKs => nothing to suggest
+	if len(a.Apks) == 0 {
+		return nil
+	}
+
+	// First, try to follow CV
+	apks := a.ApksByVName(a.SuggestedVName())
+	if len(apks) > 0 {
+		return apks
+	}
+
+	// When CV is missing current version code or it's invalid (no APKs
+	// match it), use heuristic: find all APKs having the same version
+	// string as the APK with the greatest version code
+	return a.ApksByVName(a.Apks[0].VName)
+}
+
+func (a *App) SuggestedApk(device *adb.Device) *Apk {
+	for i := range a.Apks {
+		apk := &a.Apks[i]
+		if a.CVCode >= apk.VCode && apk.IsCompatible(device) {
+			return apk
 		}
 	}
-	if len(a.Apks) > 0 {
-		return &a.Apks[0]
+	for i := range a.Apks {
+		apk := &a.Apks[i]
+		if apk.IsCompatible(device) {
+			return apk
+		}
 	}
 	return nil
 }