You can reduce the quality of a JPEG to reduce its file size. This does not affect its dimensions. Here's an ImageMagick based method I have that reduces an image's quality step-wise until it hits a given target size. Note that when reducing quality you want to start with the same image each time -- not reduce one that's already been reduced. Doing the latter will lead to very poor quality.

use File::Copy;
use Image::Magick;

sub compress_image
{
    my $image_file = shift;
    my $desired_size = shift;
    my $target_file = shift;
    my $min_quality = shift;
    my $step = shift;
    my $verbose_level = shift;
    my $image;
    my $status;
    my $size;
    my $quality;
    my $last_quality;
    local *IMAGE;
    my $blob;

    die __PACKAGE__ . " compress_image() required image file name miss
+ing.\n"
      if (!defined($image_file));
    die __PACKAGE__ . " compress_image() required image file size miss
+ing.\n"
      if (!defined($desired_size));

    $target_file = $image_file if (!defined($target_file));
    $min_quality = 1 if (!defined($min_quality));

    if (!defined($step))
    {
        $step = 5;
    }
    elsif ($step < 0)
    {
        $step = -$step;
    }

    die "Can't compress $image_file: No such file or directory.\n"
      if (! -e $image_file);

    if ($verbose_level > 0)
    {
        print "Compressing $image_file.\n";
        print "Resulting image will be in $target_file.\n";
    }

    $image = Image::Magick->new();
    $status = $image->Read($image_file);
    warn "$status" if "$status";

    $size = $image->Get('filesize');
    $last_quality = $quality = $image->Get('quality');

    if ($verbose_level > 1)
    {
        print "Initial image size:    $size\n";
        print "Initial image quality: $quality\n";
    }

    while ( ($size > $desired_size) && ($size > 0) &&
            (($quality -= $step) >= $min_quality) )
    {
        $blob = $image->ImageToBlob(quality => $quality);
        $size = length($blob);
        $last_quality = $quality;

        if ($verbose_level > 1)
        {
            print "Current image size:    $size\n";
            print "Current image quality: $quality\n";

        }
    }

    $size = $image->Get('filesize');

    if ($verbose_level > 1)
    {
        print "Final image size:      $size\n";
        print "Final image quality:   $last_quality\n";
    }

    undef $image;

    if (defined($blob))
    {
        open(IMAGE, ">$target_file") or die
          "Can't open $target_file for writing: $!\n";
        print IMAGE $blob;
        close(IMAGE) or die "Failed to close $target_file: $!\n";
    }
    elsif ($image_file ne $target_file)
    {
        copy($image_file, $target_file) or
          die "Failed to copy $image_file to $target_file: $!\n";
    }

    return ( ($size > 0) && ($size <= $desired_size) ) ? 1 : 0;
}
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