diff --git a/Configurations/common.tmpl b/Configurations/common.tmpl
index d811a2a144..5fd6b9729c 100644
--- a/Configurations/common.tmpl
+++ b/Configurations/common.tmpl
@@ -9,15 +9,22 @@
  # there are no duplicate dependencies and that they are in the
  # right order.  This is especially used to sort the list of
  # libraries that a build depends on.
+ sub extensionlesslib {
+     my @result = map { $_ =~ /(\.a)?$/; $` } @_;
+     return @result if wantarray;
+     return $result[0];
+ }
  sub resolvedepends {
      my $thing = shift;
+     my $extensionlessthing = extensionlesslib($thing);
      my @listsofar = @_;    # to check if we're looping
-     my @list = @{$unified_info{depends}->{$thing}};
+     my @list = @{$unified_info{depends}->{$extensionlessthing}};
      my @newlist = ();
      if (scalar @list) {
          foreach my $item (@list) {
+             my $extensionlessitem = extensionlesslib($item);
              # It's time to break off when the dependency list starts looping
-             next if grep { $_ eq $item } @listsofar;
+             next if grep { extensionlesslib($_) eq $extensionlessitem } @listsofar;
              push @newlist, $item, resolvedepends($item, @listsofar, $item);
          }
      }
@@ -28,8 +35,9 @@
      my @newlist = ();
      while (@list) {
          my $item = shift @list;
+         my $extensionlessitem = extensionlesslib($item);
          push @newlist, $item
-             unless grep { $item eq $_ } @list;
+             unless grep { $extensionlessitem eq extensionlesslib($_) } @list;
      }
      @newlist;
  }
diff --git a/Configurations/descrip.mms.tmpl b/Configurations/descrip.mms.tmpl
index 5a6e8d1d48..cde5144a69 100644
--- a/Configurations/descrip.mms.tmpl
+++ b/Configurations/descrip.mms.tmpl
@@ -525,6 +525,17 @@ configdata.pm : $(SRCDIR)Configure $(SRCDIR)config.com {- join(" ", @{$config{bu
   use File::Basename;
   use File::Spec::Functions qw/abs2rel rel2abs catfile catdir/;
 
+  # Helper function to figure out dependencies on libraries
+  # It takes a list of library names and outputs a list of dependencies
+  sub compute_lib_depends {
+      if ($disabled{shared}) {
+          return map { $_ =~ /\.a$/ ? $`.".OLB" : $_.".OLB" } @_;
+      }
+      return map { $_ =~ /\.a$/
+                   ? $`.".OLB"
+                   : $unified_info{sharednames}->{$_}.".EXE" } @_;
+  }
+
   sub generatesrc {
       my %args = @_;
       my $generator = join(" ", @{$args{generator}});
@@ -627,9 +638,7 @@ EOF
       my $libd = dirname($lib);
       my $libn = basename($lib);
       (my $mkdef_key = $libn) =~ s/^${osslprefix_q}lib([^0-9]*)\d*/$1/i;
-      my @deps = map {
-          $disabled{shared} ? $_.".OLB"
-              : $unified_info{sharednames}->{$_}.".EXE"; } @{$args{deps}};
+      my @deps = compute_lib_depends(@{$args{deps}});
       my $deps = join(", -\n\t\t", @deps);
       my $shlib_target = $disabled{shared} ? "" : $target{shared_target};
       my $ordinalsfile = defined($args{ordinals}) ? $args{ordinals}->[1] : "";
@@ -675,9 +684,7 @@ EOF
       my $libn = basename($lib);
       (my $libn_nolib = $libn) =~ s/^lib//;
       my @objs = map { "$_.OBJ" } @{$args{objs}};
-      my @deps = map {
-          $disabled{shared} ? $_.".OLB"
-              : $unified_info{sharednames}->{$_}.".EXE"; } @{$args{deps}};
+      my @deps = compute_lib_depends(@{$args{deps}});
       my $deps = join(", -\n\t\t", @objs, @deps);
       my $shlib_target = $disabled{shared} ? "" : $target{shared_target};
       my $engine_opt = abs2rel(rel2abs(catfile($config{sourcedir},
@@ -727,9 +734,7 @@ EOF
       my $bind = dirname($bin);
       my $binn = basename($bin);
       my @objs = map { "$_.OBJ" } @{$args{objs}};
-      my @deps = map {
-          $disabled{shared} ? $_.".OLB"
-              : $unified_info{sharednames}->{$_}.".EXE"; } @{$args{deps}};
+      my @deps = compute_lib_depends(@{$args{deps}});
       my $deps = join(", -\n\t\t", @objs, @deps);
       # The "[]" hack is because in .OPT files, each line inherits the
       # previous line's file spec as default, so if no directory spec
diff --git a/Configurations/unix-Makefile.tmpl b/Configurations/unix-Makefile.tmpl
index 1c85637f49..84ceb76365 100644
--- a/Configurations/unix-Makefile.tmpl
+++ b/Configurations/unix-Makefile.tmpl
@@ -844,13 +844,13 @@ configdata.pm: $(SRCDIR)/Configure $(SRCDIR)/config {- join(" ", @{$config{build
   # It takes a list of library names and outputs a list of dependencies
   sub compute_lib_depends {
       if ($disabled{shared}) {
-          return map { $_.$libext } @_;
+          return map { $_ =~ /\.a$/ ? $`.$libext : $_.$libext } @_;
       }
 
       # Depending on shared libraries:
       # On Windows POSIX layers, we depend on {libname}.dll.a
       # On Unix platforms, we depend on {shlibname}.so
-      return map { shlib_simple($_) } @_;
+      return map { $_ =~ /\.a$/ ? $`.$libext : shlib_simple($_) } @_;
   }
 
   sub generatesrc {
@@ -1073,11 +1073,16 @@ EOF
       my $binn = basename($bin);
       my $objs = join(" ", map { $_.$objext } @{$args{objs}});
       my $deps = join(" ",compute_lib_depends(@{$args{deps}}));
-      my $linklibs = join("", map { my $d = dirname($_);
-                                    my $f = basename($_);
-                                    $d = "." if $d eq $f;
-                                    (my $l = $f) =~ s/^lib//;
-                                    " -L$d -l$l" } @{$args{deps}});
+      my $linklibs = join("", map { if ($_ =~ /\.a$/) {
+                                        " $_";
+                                    } else {
+                                        my $d = dirname($_);
+                                        my $f = basename($_);
+                                        $d = "." if $d eq $f;
+                                        (my $l = $f) =~ s/^lib//;
+                                        " -L$d -l$l"
+                                    }
+                                  } @{$args{deps}});
       my $shlib_target = $disabled{shared} ? "" : $target{shared_target};
       my $cc = '$(CC)';
       my $cflags = '$(CFLAGS) $(BIN_CFLAGS)';
diff --git a/Configurations/windows-makefile.tmpl b/Configurations/windows-makefile.tmpl
index a0ee953dc6..d7441107c9 100644
--- a/Configurations/windows-makefile.tmpl
+++ b/Configurations/windows-makefile.tmpl
@@ -347,8 +347,10 @@ configdata.pm: "$(SRCDIR)\Configure" {- join(" ", map { '"'.$_.'"' } @{$config{b
  # It takes a list of library names and outputs a list of dependencies
  sub compute_lib_depends {
      if ($disabled{shared}) {
-	 return map { $_.$libext } @_;
+	 return map { $_ =~ /\.a$/ ? $`.$libext : $_.$libext } @_;
      }
+     die "Linking with static OpenSSL libraries is not supported in this configuration\n"
+         if grep /\.a$/, @_;
      return map { shlib_import($_) } @_;
  }
 
diff --git a/Configure b/Configure
index 3289e9f1a7..307b1d8ac4 100755
--- a/Configure
+++ b/Configure
@@ -1856,9 +1856,16 @@ EOF
                     $d = cleanfile($buildd, $_, $blddir);
                 }
                 # Take note if the file to depend on is being renamed
+                # Take extra care with files ending with .a, they should
+                # be treated without that extension, and the extension
+                # should be added back after treatment.
+                $d =~ /(\.a)?$/;
+                my $e = $1 // "";
+                $d = $`;
                 if ($unified_info{rename}->{$d}) {
                     $d = $unified_info{rename}->{$d};
                 }
+                $d .= $e;
                 $unified_info{depends}->{$ddest}->{$d} = 1;
                 # If we depend on a header file or a perl module, let's make
                 # sure it can get included