diff --git a/src/FileNames.cpp b/src/FileNames.cpp
index 82adcfa4a..f5f258aee 100644
--- a/src/FileNames.cpp
+++ b/src/FileNames.cpp
@@ -49,6 +49,102 @@ used throughout Audacity into this one place.
 
 static wxString gDataDir;
 
+const FileNames::FileType
+     FileNames::AllFiles{ XO("All files"), { wxT("") } }
+     /* i18n-hint an Audacity project is the state of the program, stored as
+     files that can be reopened to resume the session later */
+   , FileNames::AudacityProjects{ XO("Audacity projects"), { wxT("aup") }, true }
+   , FileNames::DynamicLibraries{
+#if defined(__WXMSW__)
+      XO("Dynamically Linked Libraries"), { wxT("dll") }, true
+#elif defined(__WXMAC__)
+      XO("Dynamic Libraries"), { wxT("dylib") }, true
+#else
+      XO("Dynamically Linked Libraries"), { wxT("so*") }, true
+#endif
+     }
+   , FileNames::TextFiles{ XO("Text files"), { wxT("txt") }, true }
+   , FileNames::XMLFiles{ XO("XML files"), { wxT("xml"), wxT("XML") }, true }
+;
+
+wxString FileNames::FormatWildcard( const FileTypes &fileTypes )
+{
+   // |-separated list of:
+   // [ Description,
+   //   ( if appendExtensions, then ' (', globs, ')' ),
+   //   '|',
+   //   globs ]
+   // where globs is a ;-separated list of filename patterns, which are
+   // '*' for an empty extension, else '*.' then the extension
+   // Only the part before | is displayed in the choice drop-down of file
+   // dialogs
+   //
+   // Exceptional case: if there is only one type and its description is empty,
+   // then just give the globs with no |
+   // Another exception: an empty description, when there is more than one
+   // type, is replaced with a default
+   // Another exception:  if an extension contains a dot, it is interpreted as
+   // not really an extension, but a literal filename
+
+   const wxString dot{ '.' };
+   const auto makeGlobs = [&dot]( const FileExtensions &extensions ){
+      wxString globs;
+      for ( const auto &extension: extensions ) {
+         if ( !globs.empty() )
+            globs += ';';
+         if ( extension.Contains( dot ) )
+            globs += extension;
+         else {
+            globs += '*';
+            if ( !extension.empty() ) {
+               globs += '.';
+               globs += extension;
+            }
+         }
+      }
+      return globs;
+   };
+
+   const auto defaultDescription = []( const FileExtensions &extensions ){
+      // Assume extensions is not empty
+      wxString exts = extensions[0];
+      for (size_t ii = 1, size = extensions.size(); ii < size; ++ii ) {
+         exts += XO(", ").Translation();
+         exts += extensions[ii];
+      }
+      /* i18n-hint a type or types such as "txt" or "txt, xml" will be
+         substituted for %s */
+      return XO("%s files").Format( exts );
+   };
+
+   if ( fileTypes.size() == 1 && fileTypes[0].description.empty() ) {
+      return makeGlobs( fileTypes[0].extensions );
+   }
+   else {
+      wxString result;
+      for ( const auto &fileType : fileTypes ) {
+         const auto &extensions = fileType.extensions;
+         if (extensions.empty())
+            continue;
+
+         if (!result.empty())
+            result += '|';
+
+         const auto globs = makeGlobs( extensions );
+
+         auto mask = fileType.description;
+         if ( mask.empty() )
+           mask = defaultDescription( extensions );
+         if ( fileType.appendExtensions )
+            mask.Join( XO("(%s)").Format( globs ), " " );
+         result += mask.Translation();
+         result += '|';
+         result += globs;
+      }
+      return result;
+   }
+}
+
 bool FileNames::CopyFile(
    const FilePath& file1, const FilePath& file2, bool overwrite)
 {
diff --git a/src/FileNames.h b/src/FileNames.h
index bdb3b597b..f2431dbd6 100644
--- a/src/FileNames.h
+++ b/src/FileNames.h
@@ -16,6 +16,7 @@
 #include <wx/dir.h> // for wxDIR_FILES
 #include <wx/string.h> // function return value
 #include "audacity/Types.h"
+#include "MemoryX.h"
 
 class wxFileName;
 class wxFileNameWrapper;
@@ -25,6 +26,37 @@ class wxFileNameWrapper;
 class AUDACITY_DLL_API FileNames
 {
 public:
+   // A description of a type of file
+   struct FileType {
+      FileType() = default;
+
+      FileType( TranslatableString d, FileExtensions e, bool a = false )
+         : description{ std::move( d ) }
+         , extensions( std::move( e ) )
+         , appendExtensions{ a }
+      {}
+
+      TranslatableString description;
+      FileExtensions extensions;
+      // Whether to extend the displayed description with mention of the
+      // extensions:
+      bool appendExtensions = false;
+   };
+
+   // Frequently used types
+   static const FileType
+        AllFiles // *
+      , AudacityProjects // *.aup
+      , DynamicLibraries // depends on the operating system
+      , TextFiles // *.txt
+      , XMLFiles; // *.xml, *.XML
+   
+   using FileTypes = std::vector< FileType >;
+
+   // Convert fileTypes into a single string as expected by wxWidgets file
+   // selection dialog
+   static wxString FormatWildcard( const FileTypes &fileTypes );
+
    // This exists to compensate for bugs in wxCopyFile:
    static bool CopyFile(
       const FilePath& file1, const FilePath& file2, bool overwrite = true);
diff --git a/src/import/Import.cpp b/src/import/Import.cpp
index fda4d7d9d..a64452397 100644
--- a/src/import/Import.cpp
+++ b/src/import/Import.cpp
@@ -41,6 +41,7 @@ and ImportLOF.cpp.
 #include "ImportPlugin.h"
 
 #include <algorithm>
+#include <unordered_set>
 
 #include <wx/textctrl.h>
 #include <wx/string.h>
@@ -145,6 +146,78 @@ void Importer::GetSupportedImportFormats(FormatList *formatList)
    }
 }
 
+FileNames::FileTypes
+Importer::GetFileTypes( const FileNames::FileType &extraType )
+{
+   // Construct the filter
+   FileNames::FileTypes fileTypes{
+      FileNames::AllFiles,
+      // Will fill in the list of extensions later:
+      { XO("All supported files"), {} }
+   };
+
+   if ( !extraType.extensions.empty() )
+      fileTypes.push_back( extraType );
+   
+   FormatList l;
+   GetSupportedImportFormats(&l);
+   
+   using ExtensionSet = std::unordered_set< FileExtension >;
+   FileExtensions allList = extraType.extensions, newList;
+   ExtensionSet allSet{ allList.begin(), allList.end() }, newSet;
+   for ( const auto &format : l ) {
+      newList.clear();
+      newSet.clear();
+      for ( const auto &extension : format.formatExtensions ) {
+         if ( newSet.insert( extension ).second )
+            newList.push_back( extension );
+         if ( allSet.insert( extension ).second )
+            allList.push_back( extension );
+      }
+      fileTypes.push_back( { format.formatName, newList } );
+   }
+
+   fileTypes[1].extensions = allList;
+   return fileTypes;
+}
+
+void Importer::SetLastOpenType( const FileNames::FileType &type )
+{
+   // PRL:  Preference key /LastOpenType, unusually, stores a localized
+   // string!
+   // The bad consequences of a change of locale are not severe -- only that
+   // a default choice of file type for an open dialog is not remembered
+   gPrefs->Write(wxT("/LastOpenType"), type.description.Translation());
+   gPrefs->Flush();
+}
+
+void Importer::SetDefaultOpenType( const FileNames::FileType &type )
+{
+   // PRL:  Preference key /DefaultOpenType, unusually, stores a localized
+   // string!
+   // The bad consequences of a change of locale are not severe -- only that
+   // a default choice of file type for an open dialog is not remembered
+   gPrefs->Write(wxT("/DefaultOpenType"), type.description.Translation());
+   gPrefs->Flush();
+}
+
+size_t Importer::SelectDefaultOpenType( const FileNames::FileTypes &fileTypes )
+{
+   wxString defaultValue;
+   if ( !fileTypes.empty() )
+      defaultValue = fileTypes[0].description.Translation();
+
+   wxString type = gPrefs->Read(wxT("/DefaultOpenType"), defaultValue);
+   // Convert the type to the filter index
+   auto begin = fileTypes.begin();
+   auto index = std::distance(
+      begin,
+      std::find_if( begin, fileTypes.end(),
+         [&type](const FileNames::FileType &fileType){
+            return fileType.description.Translation() == type; } ) );
+   return (index == fileTypes.size()) ? 0 : index;
+}
+
 void Importer::StringToList(wxString &str, wxString &delims, wxArrayString &list, wxStringTokenizerMode mod)
 {
    wxStringTokenizer toker;
@@ -389,10 +462,6 @@ bool Importer::Import(const FilePath &fName,
 
       for (const auto &plugin : sImportPluginList())
       {
-         // PRL:  Preference keys /DefaultOpenType and /LastOpenType, unusually,
-         // store localized strings!
-         // The bad consequences of a change of locale are not severe -- only that
-         // a default choice of file type for an open dialog is not remembered
          if (plugin->GetPluginFormatDescription().Translation() == type )
          {
             // This plugin corresponds to user-selected filter, try it first.
diff --git a/src/import/Import.h b/src/import/Import.h
index f56a4f3b3..8cff8cc85 100644
--- a/src/import/Import.h
+++ b/src/import/Import.h
@@ -18,6 +18,7 @@
 #include <wx/tokenzr.h> // for enum wxStringTokenizerMode
 
 #include "../widgets/wxPanelWrapper.h" // to inherit
+#include "../FileNames.h" // for FileType
 
 class wxArrayString;
 class wxListBox;
@@ -120,6 +121,31 @@ public:
     */
    void GetSupportedImportFormats(FormatList *formatList);
 
+   /**
+    * Constructs a list of types, for use by file opening dialogs, that includes
+    * all supported file types
+    */
+   FileNames::FileTypes
+   GetFileTypes( const FileNames::FileType &extraType = {} );
+
+   /**
+    * Remember a file type in preferences
+    */
+   static void
+   SetLastOpenType( const FileNames::FileType &type );
+
+   /**
+    * Remember a file type in preferences
+    */
+   static void
+   SetDefaultOpenType( const FileNames::FileType &type );
+
+   /**
+    * Choose index of preferred type
+    */
+   static size_t
+   SelectDefaultOpenType( const FileNames::FileTypes &fileTypes );
+
    /**
     * Reads extended import filters from gPrefs into internal
     * list mExtImportItems