diff --git a/build.sbt b/build.sbt
index 2985740..cf3ca66 100644
--- a/build.sbt
+++ b/build.sbt
@@ -1,5 +1,8 @@
 val buildName = "jardiff"
 
+val scala212Version = "2.12.18"
+val scala213Version = "2.13.12"
+
 inThisBuild(Seq[Setting[_]](
   organization := "com.lightbend",
   scalaVersion := "2.13.12",
@@ -49,6 +52,8 @@ lazy val root = (
   settings(
     name := buildName,
     publish / skip := true,
+    // See https://github.com/sbt/sbt/issues/4262#issuecomment-405607763
+    crossScalaVersions := Seq.empty
   )
 )
 
@@ -66,7 +71,9 @@ lazy val core = project.
       "ch.qos.logback" % "logback-classic" % "1.3.11",
       "org.scalatest" %% "scalatest" % "3.2.17" % Test,
     ),
-    name := buildName + "-core"
+    name := buildName + "-core",
+    crossScalaVersions := Seq(scala212Version, scala213Version),
+    scalaVersion := scala212Version
   )
 
 lazy val cli = project.
@@ -80,6 +87,11 @@ lazy val cli = project.
       case x if x.endsWith("module-info.class") => MergeStrategy.discard
       case x => (assembly / assemblyMergeStrategy).value(x)
     },
+    // Having Scala 2.13 here in crossScalaVersions is redundant but due to how
+    // sbt-github-actions generates the sbt test command (i.e. sbt '++ 2.13.12' test),
+    // sbt's update task cannot handle projects with different crossScalaVersions well
+    crossScalaVersions := Seq(scala212Version, scala213Version),
+    scalaVersion := scala212Version,
     // cli is not meant to be published
     publish / skip := true,
   ).dependsOn(core)
diff --git a/cli/src/main/scala/scala/tools/jardiff/Main.scala b/cli/src/main/scala/scala/tools/jardiff/Main.scala
index cdf08b9..36e5df7 100644
--- a/cli/src/main/scala/scala/tools/jardiff/Main.scala
+++ b/cli/src/main/scala/scala/tools/jardiff/Main.scala
@@ -4,6 +4,8 @@
 
 package scala.tools.jardiff
 
+import JDKCollectionConvertersCompat.Converters._
+
 import java.io.{ByteArrayOutputStream, File, PrintWriter}
 import java.nio.file._
 
@@ -11,7 +13,6 @@ import org.apache.commons.cli
 import org.apache.commons.cli.{CommandLine, DefaultParser, HelpFormatter, Options}
 import org.eclipse.jgit.util.io.NullOutputStream
 
-import scala.jdk.CollectionConverters._
 import scala.util.Try
 import scala.util.control.NonFatal
 
diff --git a/core/src/main/scala/scala/tools/jardiff/AsmTextifyRenderer.scala b/core/src/main/scala/scala/tools/jardiff/AsmTextifyRenderer.scala
index c7b65a6..fefa357 100644
--- a/core/src/main/scala/scala/tools/jardiff/AsmTextifyRenderer.scala
+++ b/core/src/main/scala/scala/tools/jardiff/AsmTextifyRenderer.scala
@@ -4,10 +4,11 @@
 
 package scala.tools.jardiff
 
+import JDKCollectionConvertersCompat.Converters._
+
 import java.io.PrintWriter
 import java.nio.file.{Files, Path}
 
-import scala.jdk.CollectionConverters._
 import org.objectweb.asm.{ClassReader, Opcodes}
 import org.objectweb.asm.tree.{ClassNode, FieldNode, InnerClassNode, MethodNode}
 import org.objectweb.asm.util.TraceClassVisitor
diff --git a/core/src/main/scala/scala/tools/jardiff/JDKCollectionConvertersCompat.scala b/core/src/main/scala/scala/tools/jardiff/JDKCollectionConvertersCompat.scala
new file mode 100644
index 0000000..0cf4ebb
--- /dev/null
+++ b/core/src/main/scala/scala/tools/jardiff/JDKCollectionConvertersCompat.scala
@@ -0,0 +1,31 @@
+package scala.tools.jardiff
+
+import scala.annotation.nowarn
+
+/** Magic to get cross-compiling access to `scala.jdk.CollectionConverters`
+ *  with a fallback on `scala.collection.JavaConverters`, without deprecation
+ *  warning in any Scala version.
+ *
+ *  @see https://github.com/scala/scala-collection-compat/issues/208
+ */
+@nowarn("msg=Unused import")
+private[jardiff] object JDKCollectionConvertersCompat {
+  object Scope1 {
+    object jdk {
+      type CollectionConverters = Int
+    }
+  }
+  import Scope1._
+
+  object Scope2 {
+    import scala.collection.{JavaConverters => CollectionConverters}
+
+    object Inner {
+      import scala._
+      import jdk.CollectionConverters
+      val Converters = CollectionConverters
+    }
+  }
+
+  val Converters = Scope2.Inner.Converters
+}
diff --git a/core/src/main/scala/scala/tools/jardiff/JarDiff.scala b/core/src/main/scala/scala/tools/jardiff/JarDiff.scala
index d96301c..8b14603 100644
--- a/core/src/main/scala/scala/tools/jardiff/JarDiff.scala
+++ b/core/src/main/scala/scala/tools/jardiff/JarDiff.scala
@@ -4,6 +4,8 @@
 
 package scala.tools.jardiff
 
+import JDKCollectionConvertersCompat.Converters._
+
 import java.io.{File, OutputStream}
 import java.nio.file._
 import java.nio.file.attribute.BasicFileAttributes
@@ -14,7 +16,6 @@ import org.eclipse.jgit.lib.RepositoryCache
 import org.eclipse.jgit.revwalk.RevCommit
 
 import scala.tools.jardiff.JGitUtil._
-import scala.jdk.CollectionConverters._
 
 final class JarDiff(files: List[List[Path]], config: JarDiff.Config, renderers: String => List[FileRenderer]) {
   private val targetBase = config.gitRepo.getOrElse(Files.createTempDirectory("jardiff-"))